Special equipment: a 10-inch springform pan and a pizza cutter
For the dough: Warm the milk and 1/2 cup of water in a small saucepan over low heat until a thermometer registers 100 to 110 degrees F. Remove from the heat and sprinkle the yeast and a pinch of granulated sugar over top. Set aside undisturbed until foamy, about 5 minutes.
Whisk together the salt, 2 3/4 cups flour and remaining granulated sugar in a large bowl. Generously butter a 10-inch springform pan.
Combine the melted butter, vanilla and egg yolk in the bowl of an electric mixer fitted with a paddle attachment and mix on low until combined. Add the yeast mixture and continue to mix on low until combined. Add the flour mixture and mix on low until a thick and slightly sticky dough forms. Once the dough comes together, switch to the dough hook and knead on medium speed, adding up to 1/4 cup more flour if needed, to make a soft, smooth ball that sticks to the hook, 3 to 4 minutes.
Coat a large bowl generously with cooking spray. Add the dough, turning to coat. Cover with plastic wrap and let rise at room temperature until the dough is doubled in size, about 1 hour.
For the filling: Meanwhile, heat a large skillet over medium-high heat. Add the butter and cook, swirling, until melted. Add the diced apples and cook, stirring occasionally, until tender, about 8 minutes. Turn off the heat and stir in the apple butter. Transfer to a medium bowl to cool completely.
When the dough is ready, punch it down and turn out onto a lightly floured surface. Knead a few times, then roll into a rectangle 12 inches by 18 inches, keeping the longer side closest to you. Spread the cooled apple filling evenly all over the dough. Sprinkle with the granulated sugar. Use a pizza cutter to cut the dough crosswise into 1-inch strips. Starting on the left side, roll 1 strip up jelly roll style. When you get to the end, press another strip to the first one and continue rolling. Repeat this with 2 more strips. Carefully transfer the rolled dough to the center of the prepared pan. The spiral should be facing up. Continue coiling the remaining strips of dough filling-side in around the middle roll until the pan is filled. This might get messy, but that's part of the fun. Loosely cover the pan with plastic wrap and let rise until doubled in size, about 30 minutes.
Position an oven rack in the center of the oven and preheat to 350 degrees F. Bake until the cinnamon roll is puffed and golden brown, about 50 minutes. Let cool on a rack for 10 minutes.
For the glaze: Meanwhile, microwave the cream cheese in a microwave-safe bowl until softened, 10 to 15 seconds. Add the confectioners' sugar and milk and whisk until smooth.
Remove the outer ring from the springform pan. Pour the glaze on top of the cinnamon roll, then use a spatula to spread it all over. Cut into 8 to 10 wedges.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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