In a small saucepan over low-medium heat, cook together 3 tablespoons milk with 2 tablespoons of flour, whisking constantly, until a thick paste forms. Remove and cool completely. In a microwave safe bowl, heat together the remaining 3/4 cup whole milk with the brown sugar until it is about 110 degrees, or warm to the touch. Stir in the yeast, and set aside until puffy and bloomed.

In the bowl of your stand mixer, mix together the egg and softened butter, and then stir in the bloomed yeast mixture. Then add in 3 cups flour and the salt, and stir until a shaggy dough forms. Add in the cooked flour paste and begin to knead the dough.

Knead the dough with the dough hook for about 10 minutes or until the dough is soft and smooth. It should be still a little tacky, and may stick to the bottom of your bowl slightly while kneading. Avoid adding too much flour, but you can add a bit more if it’s just globbing entirely on the bottom of the bowl.

Scrape the dough into a ball, and cover the bowl with plastic wrap. Let the dough rise for about 30 minutes, or until it has almost doubled in size.

Peel and chop your apples into bite-sized chunks. Place the apples in a medium sauce pan along with 1/4 cup brown sugar and 1 tsp. cinnamon, stirring until everything is coated. Cook over medium heat for about 10 minutes, stirring occasionally, until the apples have softened

Grease a 9×9 square pan or a round 9 inch cake pan and set aside. In a small bowl, stir together the brown sugar, sugar, cinnamon, and salt until combined. Roll out the risen dough into a large rectangle. It should be about 12-14 inches long. Spread the butter evenly over the entire dough. Once the apple filling is cooled, drain out the extra liquid from the bottom of the pan. Stir in the additional brown sugar and cinnamon until everything is well coated. Evenly spread the apple mixture over the butter mixture in your rolls.

Gently roll the dough lengthwise into a long log. This process might be a little messy, but they do not have to be perfect so don't stress it.

Slice the ends of the log off, and then slice the log into 9 even rolls. The dough is soft to work with, so you may find the rolls get a little messy or unraveled, but you can re-roll them individually if needed. Place into your prepared baking pan, and cover with plastic wrap to let them rise for about 20 minutes, or until puffed.

Meanwhile, preheat your oven to 350 degrees. Bake the risen rolls for about 25-30 minutes, or until they are light golden brown on top.

Beat together the cream cheese, powdered sugar, milk, vanilla extract, cinnamon, and salt until a thick, smooth frosting is formed. Spread generously on top of the rolls once they have cooled for about 5 minutes. Enjoy the frosted rolls warm!