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1
Make the dough: Pour the cool water into the bowl of a stand mixer fitted with the bread hook. Crumble the yeast into the water and use your fingers to rub and dissolve it; if using active dry yeast, whisk the yeast into the water. Add the flour, eggs, sugar, salt, and oil.
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2
Mix the dough on low speed to combine the ingredients, stopping the mixer if the dough climbs up the hook or if you need to work in dry ingredients that have settled on the bottom of the bowl. Scrape the bottom and sides of the bowl as needed. It should take about 2 minutes for the dough to come together. If there are lots of dry bits in the bottom of the bowl that just aren't getting worked in, add a tablespoon or two of water. On the other hand, if the dough feels very soft, add a few pinches of flour.
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3
Note: Eventually you'll be able to feel the dough and know if you need to add water or flour; it's always better to adjust the ratios when the dough is first coming together at the beginning of mixing rather than wait until the end of the kneading process, since it takes longer for ingredient additions to get worked into the dough mass at this later point and you risk overworking the dough.
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4
Increase the speed to medium and knead until a smooth dough forms, about 4 minutes. You want the dough to be a bit firm.
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5
Stretch and fold the dough: Lightly dust your work surface with a little flour, and use a dough scraper to transfer the dough from the mixing bowl to the floured surface. Use your palms to push and tear the top of the dough away from you in one stroke, and then fold that section onto the middle of the dough. Give the dough a quarter turn and repeat the push/tear/fold process for about 1 minute. Then push and pull the dough against the work surface to round it into a ball.
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6
Let the dough rise: Lightly dust a bowl with flour, add the dough, sprinkle just a little flour on top of the dough, and cover the bowl with plastic wrap. Set the bowl aside at room temperature.
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7
Once the dough has risen by 70% (after about 40 minutes, depending on how warm your room is), divide the dough in half and gently press each piece into a square. Wrap them individually in plastic wrap and refrigerate for 1 hour.
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8
While the dough chills, make the filling: Place the butter, brown sugar, granulated sugar, and cinnamon in the bowl of a stand mixer fitted with the paddle attachment, and cream the mixture on low speed until it is combined. Scrape down the bottom and sides of the bowl as needed and continue to beat until well combined without creating any volume, about 30 seconds.
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9
Fill the dough: Remove 1 square of dough from the refrigerator and place it on a lightly floured work surface. Press or roll the dough into a 12-inch square, and then spread 1/2 cup of the cinnamon-sugar filling over the left half of the dough. Fold the right side of the dough over the left so the edges meet, and then use a rolling pin to roll and lightly flatten the dough. Wrap in plastic wrap and refrigerate while you repeat with the second piece of dough. Refrigerate the second piece.
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10
Place the first piece of dough on the lightly floured work surface so the seam is at the top. Roll the dough to a 12-inch square. Use your hand to make 2 vertical indentations in the dough, dividing it into thirds. Spread 1/2 cup of the cinnamon-sugar filling over the left-hand third of the dough. Then create a simple fold by folding the left-hand side over the middle, then the right-hand side over the middle, so the dough is folded like a business letter. Wrap in plastic wrap and refrigerate for 1 hour. Repeat with the second piece.
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11
Unwrap the first piece of dough and set it on a floured surface, seam at the top. Lightly flour the top of the dough and then roll it into a 12-inch square that is about 1/4 inch thick. Spread half the remaining cinnamon-sugar filling over the dough (leave a 1/2-inch border at the top) and then, starting at the bottom, roll the dough into a cylinder, pressing down on the seam to seal it. Repeat with the second piece of dough.
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12
Shape the dough: Place the cylinders onto a parchment paper-lined rimmed sheet pan. Starting at the top of one of the cylinders, use kitchen scissors to slice the dough on an angle and in 1-inch alternating intervals about three-quarters of the way through (so make your first snip on the left side on an angle, then the next snip on the right side on an angle, and leave the very bottom attached). Starting at the top, flip one piece over. Skip the next piece, then flip the next one over and continue. Cover the sheet pan with plastic wrap and set aside in a warm, draft-free spot to rise until they have doubled in volume, 30 to 40 minutes.
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13
Preheat the oven to 350u00b0 F.
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14
Bake the loaves: Whisk the egg, water, and salt together in a small bowl, and brush the egg wash over the challah. Bake until they are browned, 18 to 20 minutes.
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15
Meanwhile, make the simple syrup: Combine the sugar and water in a small saucepan and bring to a boil over high heat. Reduce the heat to medium-low and simmer, stirring occasionally to dissolve the sugar. Turn off the heat and set aside to cool. Remove the challah from the oven and immediately brush with the simple syrup. Cool completely on the sheet pan or serve warm.
