Warm milk in the microwave for about 45 seconds or until a thermometer reads 100 to 110 degrees. Add milk and 1 teaspoon sugar to the bowl of a stand mixer fit with a dough hook. Sprinkle the yeast over the milk and stir to combine. Let stand for about 5 minutes until the yeast starts to foam. Whisk together flour, sugar and salt in a bowl.
Add eggs, vanilla and then the dry ingredients to the yeast mixture. Mix on low speed until combined and then increase speed to medium and mix for about 5 minutes until the dough is smooth.
Add butter and mix on medium speed, about 4 minutes, until butter is incorporated and dough comes together but is sticky. Scrape down the sides of the bowl as needed during mixing.
Cover the bowl with plastic wrap and let rise in a warm place for 1 to 1 ½ hours until the dough is about doubled in size. Punch down the dough and scrape out onto a lightly floured surface.
Roll dough out into a 12 x 21 inch rectangle. Spread softened butter onto the dough all the way to the edges except one long edge leaving about a 1 inch border.
Combine the brown sugar and cinnamon in a small bowl. Sprinkle over the butter evenly and press it into the butter using your fingers or a spatula. Scatter the chopped apples over the brown sugar evenly.
Starting from the long edge without the border, roll into a tight log, pressing the seam together at the end. Cut into 12 slices about 1 ½ inches thick each.
Spray a 9 x 13 pan with baking spray and arrange the rolls in the baking pan. Cover with plastic wrap and let rise in a warm place for about an hour or until puffy and mostly touching in the pan.
Bake at 375 degrees until golden brown, about 23 minutes. Allow to cool at least 15 minutes prior to frosting the rolls so the frosting doesn't completely melt.