In a large mixing bowl (or stand mixer bowl), combine warmed milk, sugar, and yeast. Let sit for about 5 minutes until frothy.

Add melted butter, eggs, and salt to the yeast mixture. Gradually add flour while mixing until a dough begins to form. Knead for about 5-7 minutes until smooth and elastic.

Place the dough in a greased bowl, cover with a kitchen towel, and let rise in a warm place for about 1 hour or until doubled in size.

While the dough is rising, prepare the filling. In a small saucepan over medium heat, melt 1 tablespoon of butter. Add diced apples, brown sugar, cinnamon, and lemon juice. Cook for about 5-7 minutes until the apples are tender. Remove from heat and let cool.

Once the dough has risen, punch it down and turn it out onto a floured surface. Roll the dough into a rectangle about ¼ inch thick.

Spread the filled apple mixture evenly over the rolled-out dough. Roll the dough tightly from the long side into a log.

Slice the roll into 12 equal pieces and place them cut side up in a greased baking sheet lined with parchment paper.

Cover the rolls and let them rise again for about 30 minutes until puffed.

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

While the rolls bake, prepare the icing by whisking together powdered sugar, milk, and vanilla extract until smooth.

Once the rolls are done baking, let them cool for a few minutes before drizzling the icing over the top.