Prepare the Dough: In a large mixing bowl, combine the warm milk and granulated sugar. Sprinkle the yeast over the milk and let it sit for about 5 minutes, until it becomes foamy. Stir in the melted butter, vanilla extract, and eggs. Gradually add the flour and salt, mixing until a dough forms. Once combined, knead the dough for about 8-10 minutes on a lightly floured surface, or until it’s soft and elastic.

Let the Dough Rise: Place the dough in a lightly greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for 1-1.5 hours, or until it doubles in size.

Prepare the Filling: While the dough rises, prepare the apple filling. In a small saucepan, melt the butter over medium heat. Add the chopped apples, brown sugar, and cinnamon, and sauté for 5-7 minutes, until the apples soften and the mixture becomes syrupy. Remove from heat and set aside to cool.

Assemble the Rolls: Once the dough has risen, punch it down and transfer it to a floured surface. Roll the dough into a rectangle, about 12x16 inches. Spread the softened butter evenly over the dough, leaving a small border around the edges. Spoon the apple-cinnamon mixture over the buttered dough, spreading it out evenly. Starting at one long edge, tightly roll the dough into a log. Cut the log into 12 even slices.

Bake the Rolls: Arrange the sliced rolls in a greased 9x13-inch baking dish. Cover the dish with a towel and let the rolls rise for another 30-45 minutes, until puffed. Preheat your oven to 350°F (175°C). Once the rolls have risen, bake them for 20-25 minutes, or until golden brown.

Make the Glaze: While the rolls bake, whisk together the powdered sugar, milk, vanilla extract, and a pinch of salt in a small bowl until smooth. Adjust the consistency by adding more milk if you want a thinner glaze.

Glaze and Serve: Once the rolls are baked and slightly cooled, drizzle the glaze over the top. Serve warm and enjoy the cozy, comforting flavors of homemade apple cinnamon rolls.