In a small bowl, combine warm milk and 1 tablespoon of sugar. Sprinkle yeast over the top and let it sit for about 5-10 minutes until frothy. This activates the yeast.

In a large mixing bowl or stand mixer, combine the flour, remaining sugar, and salt. Mix well.

Add the melted butter, eggs, and the yeast mixture to the flour mixture. Mix on low speed until combined, then increase to medium speed and knead for about 5-7 minutes until the dough is smooth and elastic.

Form the dough into a ball and place it in a greased bowl. Cover with a clean kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.

While the dough is rising, prepare the filling. In a medium bowl, toss the diced apples with lemon juice, cinnamon, and brown sugar. Set aside to allow the flavors to meld.

Once the dough has risen, punch it down to release air. On a floured surface, roll the dough into a rectangle about ¼ inch thick.

Spread the softened butter over the dough, then evenly distribute the apple filling across the surface.

Starting from one long edge, carefully roll the dough into a tight log. Pinch the seam to seal.

Cut the log into 12 equal pieces and place them in a greased baking dish or on a parchment-lined baking sheet. Cover and let rise for another 30 minutes.

Preheat the oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until golden brown.

Remove from the oven and let cool slightly before glazing.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the milk for desired consistency.

Drizzle the glaze over the warm rolls before serving.