01 - In a large mixing bowl, dissolve the yeast in warm milk with one tablespoon of sugar. Let stand for 5 minutes until foamy.
02 - Add remaining sugar, melted butter, egg, and salt to the bowl. Stir until fully incorporated.
03 - Gradually add flour, mixing until a soft dough forms. Knead by hand or using a dough hook for 8 to 10 minutes until smooth and elastic.
04 - Transfer dough to a greased bowl, cover, and let rest in a warm area for 1 hour, or until doubled in volume.
05 - In a separate bowl, combine diced apples with brown sugar and ground cinnamon; set aside.
06 - Punch down the risen dough and roll it out onto a lightly floured surface to a 16x12 inch rectangle.
07 - Spread the softened butter evenly over the rolled dough. Distribute the apple mixture over the surface.
08 - Starting from one long side, roll dough tightly into a log. Cut into 12 equal sections.
09 - Arrange slices cut-side up in a greased 9x13 inch baking dish. Cover loosely and let rise for 30 minutes.
10 - Preheat oven to 350°F. Bake for 25 to 28 minutes until tops are golden brown.
11 - While rolls are baking, whisk together powdered sugar, milk, and vanilla extract until smooth.
12 - Drizzle glaze generously over warm rolls before serving.