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To make the dough:
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Stir together 2 cups (9 ounces/255 grams) of the flour, the sugar, yeast, salt, cardamom, nutmeg, and cinnamon in the bowl of a stand mixer; set aside.
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In a small, heavy saucepan, combine the milk and butter and heat over low heat just until the butter melts.
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Add the water and set aside until warm (120 to 130 degrees F), about 1 minute.
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Pour the milk mixture over the flour-yeast mixture and mix well with a rubber spatula until all of the dry ingredients are moistened.
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Attach the bowl to the mixer, and fit the mixer with the paddle attachment.
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With the mixer on low speed, add the eggs, one at a time, beating after each addition until incorporated.
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Add the vanilla in the final moments of mixing.
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Stop the mixer, add 1/2 cup (2 1/4 ounces/65 grams) more flour, and resume mixing on low speed until smooth, 30 to 45 seconds.
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Add 2 tablespoons additional flour and resume mixing on medium speed until the dough is smooth, still soft, and slightly sticky, about 45 seconds.
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Sprinkle the work surface with 1 tablespoon of the flour, and center the dough on the flour.
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Knead the dough gently until it is smooth and no longer sticky, adding an additional 1 to 2 tablespoons flour only if necessary to prevent stickiness.
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Place the dough in a large bowl, cover the bowl securely with plastic wrap, and let the dough rise in a warm place (70 degrees F) until doubled in bulk, 45 to 60 minutes.
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The dough is ready when a finger gently pressed into it leaves an indentation.
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Meanwhile, prepare the baking pan, the glaze, and the filling.
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To make the Butterscotch Glaze:
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Lightly coat a 9 by 2-inch round cake pan with nonstick spray, or butter the pan.
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Combine the sugar, butter, and corn syrup in a small, heavy saucepan and set over low heat until the butter is completely melted.
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Pour the mixture into the prepared pan and tilt the pan to cover the bottom evenly; set aside.
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(The glaze might thicken slightly before its time to place the dough in the pan, but it will liquefy again as the coffee cake bakes.)
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To make the Cinnamon-Butter Filling:
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In a small bowl or cup, stir the cinnamon into the butter; set aside.
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Before baking:
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Center a rack in the oven and preheat the oven to 350 degrees F.
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To assemble the coffeecake:
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Gently deflate the dough.
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On a lightly floured work surface, roll out the dough into a 16 by 12-inch rectangle.
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Using a pastry brush, spread the butter-cinnamon mixture evenly over the dough.
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Cut the dough lengthwise into six 2-inch-wide strips.
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(A pizza cutter is helpful here.)
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Loosely (so the dough has some give as it expands in the oven) roll up 1 strip and place it, cut edge up, in the center of the prepared pan on top of the glaze.
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One at a time, coil the remaining dough strips around the center strip, starting each strip at the end of the previous one, to make a single large spiral.
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As you roll the dough strips around the coffee cake, the butter-cinnamon side of the dough strips should be facing inside.
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(When you finish forming the spiral there will be plenty of space left in the pan.
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The spaces around the dough will fill in as the dough bakes.)
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Loosely cover the pan with plastic wrap and let the cake rise in a warm place until it is almost doubled in size, about 30 minutes.
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The dough is ready when a finger gently pressed into it leaves an indentation.
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Bake the coffee cake until the top is deep golden brown, about 35 minutes.
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Check after 20 minutes to make sure the cake is not browning too fast.
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If it is, cover the top loosely with aluminum foil for the last 10 to 15 minutes of baking to prevent overbrowning.
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Transfer to a wire rack (if you have used foil, remove it) and let cool for 10 minutes.
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Gently tilt the pan and tap the sides on a counter to release the cake sides, then invert a serving plate on top of the cake, and invert the pan and the plate.
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Leave the pan on the cake for 1 minute, so the glaze transfers to the cake, then gendy lift off the pan.
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Using a rubber spatula, scrape out any butterscotch syrup remaining in the pan and spread it over the warm surface of the cake.
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Serve the cake warm or at room temperature, cut into wedges gently with a serrated knife.
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This coffee cake is best eaten the day it is baked.
