1. Combine flour, granulated sugar, instant yeast, and kosher salt in a large bowl.
2. Mix together warm milk, melted butter, beaten eggs, and vanilla extract in a separate bowl.
3. Gradually combine the wet ingredients with the dry ingredients, stirring to form a dough.
4. Knead the dough on a floured surface until smooth (about 8-10 minutes).
5. Transfer the dough to a greased bowl, cover, and let it rise for 1-1.5 hours until doubled in size.
6. Prepare the cinnamon filling by combining softened butter, brown sugar, and cinnamon in a bowl to form a spreadable paste.
7. Prepare the apple filling by sautéing diced apples with lemon juice, granulated sugar, and vanilla extract in a skillet until softened. Add cornstarch to thicken the mixture and set aside to cool.
8. Roll out the risen dough into a 12×16 inch rectangle.
9. Spread the cinnamon filling evenly over the dough, leaving a border around the edges.
10. Sprinkle the apple filling over the cinnamon layer.
11. Roll the dough tightly into a log and trim the edges.
12. Cut the log into 12 equal slices and place the rolls in a greased baking dish.
13. Cover the rolls and let them rise for an additional 45-60 minutes.
14. Preheat the oven to 350°F (175°C).
15. Bake the rolls for 20-30 minutes until light golden brown.
16. Prepare the brown butter maple icing by browning butter in a saucepan over medium heat.
17. Mix the browned butter with powdered sugar, maple syrup, vanilla extract, and milk in a bowl until smooth.
18. Drizzle the glaze over the slightly cooled rolls.
19. Serve and enjoy your Apple Cinnamon Rolls with Brown Butter Maple Icing.