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1
In a large bowl of a stand mixer, stir together 1 tablespoon of granulated sugar, 1/4 cup warm (110 degrees F) water, and the yeast.
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2
Let stand until softened, about 5 minutes.
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3
Add 1 1/4 cups more warm water, the salt, 6 tablespoons of granulated sugar, the shortening, and egg.
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4
Stir just until blended.
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5
Gradually add 3 3/4 cups of the flour and beat on medium speed with a dough hook until a smooth, stretchy dough forms and it pulls away somewhat from the bowl, about 10 minutes (it will still feel quite wet).
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6
Remove the dough hook and loosely cover the bowl.
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7
Let the dough rise at room temperature until doubled, about 40 minutes.
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8
In a small bowl, combine the cinnamon with 1/2 cup plus 1 tablespoon of granulated sugar and all the brown sugar.
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9
Generously flour a large work surface and scrape the dough onto it.
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10
Generously sprinkle the dough and a rolling pin with flour.
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11
Very gently roll and pat the dough into a 10-inch by 24-inch rectangle, keeping a light coating of flour on the surface of the dough but trying not to work it in.
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12
Sprinkle with the cinnamon-sugar mixture, then roll into a log starting from one of the shorter sides.
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13
Cut the dough straight down into 8 equal slices.
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14
Place the slices cut-side up in a greased 10-inch springform pan.
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15
Let stand until puffy, about 30 minutes.
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16
Preheat the oven to 325 degrees F.
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17
Set the springform pan on a rimmed baking pan and bake until golden and a toothpick inserted into the center roll (avoid cinnamon-sugar swirls) comes out clean, about 45 minutes.
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18
Let cool in the pan on a rack, 30 minutes.
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19
Meanwhile, make the cinnamon butter: In the bowl of a stand mixer, beat the butter with 1 teaspoon cinnamon until blended.
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20
Run a knife around the inside of the pan to release the rolls; remove the pan rim.
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21
With a serrated knife, cut the rolls apart and top each with about 1 tablespoon of cinnamon butter.
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22
Put the rolls on a platter and place in a warm oven until the butter has mostly melted, about 1 minute.
