Method

• In a large mixing bowl or the bowl of a stand mixer, combine the warm milk, active dry yeast, and granulated sugar. Stir gently and let the mixture stand for 5–10 minutes, until the surface becomes foamy. If the yeast does not foam, it may be inactive or the milk may have been too hot or too cold. Start again with fresh yeast before proceeding.
• Add the melted, slightly cooled butter, egg, and vanilla extract to the yeast mixture. Whisk until combined. Add 3½ cups (438 g) of the flour and the kosher salt. Stir with a wooden spoon or mix on low speed with a dough hook until a shaggy dough forms. The dough should be soft and slightly tacky rather than dry or crumbly.
• Knead the dough in a stand mixer on medium-low speed for 6–8 minutes, or by hand on a lightly floured surface for 8–10 minutes. It should become smooth, elastic, and slightly tacky without sticking heavily to your hands. Add the reserved flour a tablespoon at a time only if the dough is too sticky to handle. Avoid adding too much flour, which can make the rolls dense.
• Shape the dough into a ball and place it in a lightly greased bowl. Cover with a clean kitchen towel or plastic wrap. Let it rise in a warm, draft-free spot for approximately 60 minutes, or until nearly doubled in size. A gentle fingertip indentation should remain briefly in the dough rather than immediately springing back.
• While the dough rises, melt 1 tablespoon (14 g) of butter in a medium skillet over medium heat. Add the finely diced apples, ¼ cup (55 g) brown sugar, 1 teaspoon cinnamon, nutmeg, and lemon juice. Cook for 5–7 minutes, stirring occasionally, until the apples begin to soften and release their juices.
• In a small bowl, stir the cornstarch into the water until smooth. Pour the mixture into the skillet and cook for another 1–2 minutes, stirring continuously, until the liquid thickens and lightly coats the apples. The filling should be moist but not watery. Remove it from the heat and spread it on a plate to cool completely while the dough finishes rising.
• In a small bowl, combine the remaining ½ cup (110 g) brown sugar with 1 tablespoon of cinnamon. Keep the softened butter separate so it can be spread evenly over the rolled dough.
• Lightly grease a 9 × 13-inch baking dish: Once the dough has risen, gently punch it down and transfer it to a lightly floured work surface. Roll it into a rectangle approximately 12 × 18 inches, with the longer edge facing you. Aim for an even thickness so the finished rolls bake uniformly.
• Spread the ¼ cup (57 g) softened butter evenly over the dough, leaving a ½-inch border along one long edge. Sprinkle the cinnamon sugar mixture evenly over the butter, then distribute the cooled apple filling across the surface. Keep the apple pieces in a fairly even layer rather than piling them in the center.
• Starting with the long edge opposite the uncovered border, roll the dough into a snug log. Pinch the seam gently to seal it. Use a sharp knife or unflavored dental floss to cut the log into 12 equal rolls, approximately 1½ inches thick. If a little apple filling escapes during cutting, tuck it back into the rolls.
• Place the rolls cut-side up in the prepared baking dish, arranging them in 3 rows of 4. Cover loosely and let rise in a warm place for 30–40 minutes, until noticeably puffy and beginning to touch. During the final 15 minutes of rising, preheat the oven to 350°F (175°C).
• Remove the covering and place the baking dish on the center oven rack. Bake for 25–30 minutes, until the tops are lightly golden and the center rolls are cooked through. The dough in the center should no longer look wet or raw. An instant-read thermometer inserted into the bread portion of a center roll should register approximately 190°F (88°C). If the tops begin browning too quickly, loosely cover the dish with aluminum foil.
• While the rolls bake, beat the softened cream cheese and butter together until smooth. Add the sifted powdered sugar and vanilla extract, then mix until creamy. Add the milk, 1 tablespoon at a time, until the glaze reaches a thick but spreadable consistency. For a thinner glaze that drips down the sides of the rolls, use the full 2 tablespoons of milk.
• Remove the baked rolls from the oven and let them cool in the pan for 10 minutes. Spread the cream cheese glaze over the warm rolls, allowing it to soften slightly and settle into the spirals. For a thicker, more distinct layer of frosting, allow the rolls to cool longer before glazing.
• Serve the Apple Pie Cinnamon Rolls warm, while the dough is soft and the apple filling is tender. Use a spatula to lift each roll from the pan, keeping the layers and filling intact.