In a small bowl, combine the warm milk, 2 tablespoons of sugar and the yeast and mix. Set aside to proof for 5 minutes. In the bowl of a stand mixer fitted with a paddle attachment, add the butter, remaining sugar, eggs and salt. Beat on medium-high speed for 2 minutes. Add the proofed yeast mixture and whisk together. Lastly, add in the flour. Using the dough hook attachment, knead the dough on medium speed for 5-6 minutes or until a smooth, elastic dough that pulls away from the side has formed and then roll into a round ball. Place into a greased bowl and cover with a damp towel or plastic wrap to proof for 1½ hours, or until doubled in size.
1 cup milk, ⅓ cup granulated sugar, 2½ teaspoons instant yeast, 2 large eggs, 1 teaspoon kosher salt, 4 cups all-purpose flour, ½ cup unsalted butter
While the dough is proofing, make the filling. Add all of the filling ingredients except for the cornstarch and ½ cup of butter to a large saucepan. Place over medium heat and whisk while the butter and sugar melt. Allow the mixture to simmer, whisking to avoid scorching, 4-8 minutes. Add the cornstarch in and whisk. Reduce the heat to medium and allow to cook down for another 10 minutes or until the sauce has turned into a caramel consistency. Remove from the heat and set aside while you roll the dough out.
5 cups chopped apples, ½ cup brown sugar, 3 tablespoons unsalted butter, 1 tablespoon lime juice, 1 tablespoon ground cinnamon, 1 teaspoon apple pie spice, ¾ teaspoon kosher salt, 1 tablespoon cornstarch
Once the dough has doubled in size, turn out onto a floured surface. Sprinkle the top of the dough with a little bit of flour and roll into a rectangle. The rectangle should be roughly 16 inches long, 12 inches wide, and about ½-inch thick. Using a pastry brush or a spoon, spread the ½ cup of butter over the entire surface of the dough. Spoon the apple filling mixture over the surface and spread. Tightly roll the dough into a log and pinch the seam together to prevent the rolls from opening. Using a sharp knife, slice the log to 10 rolls.
½ cup unsalted butter
Spray a 9x13-inch baking pan with nonstick spray. Place the cinnamon rolls into the baking pan, leaving a space of about 1½ centimeters between each roll to allow them to rise. Place into a warm area and let rise until doubled in size, about 30 minutes.
Once the rolls have doubled in size, preheat the oven to 350°F. Place the cinnamon rolls into the oven to bake for 40-45 minutes or until the edges are golden and the centers are baked through (190°F). Once baked, remove from the oven and place onto a cooling rack to cool.
While the cinnamon rolls are cooling, make the frosting by combining all of the frositng ingredients in the bowl of a stand mixer fitted with a paddle attachment. Beat on medium-high speed for 5-6 minutes or until completely smooth. While the cinnamon rolls are still warm, spoon the frosting over the top of the cinnamon rolls and serve immediately.
4 ounces cream cheese, ¼ cup unsalted butter, ½ cup powdered sugar, 1 tablespoon milk, 1 teaspoon pure vanilla extract