For the filling, melt butter in a skillet over medium heat. Add diced apples, brown sugar, granulated sugar, cinnamon, nutmeg, and lemon juice. Cook for 6–8 minutes, stirring gently with a soft spatula every few minutes, until apples soften and release juices. In a small bowl, stir together cornstarch and water, then add to the pan and mix to combine. Cook 1–2 minutes until thickened. Remove from heat and cool completely.

For dough, combine the flour, sugar and salt in a stand mixer bowl if kneading by machine or standard medium bowl if kneading by hand. Set aside. Add milk and butter to a small microwave safe bowl. Warm to about 90-110°F (32-43°C) on an instant read thermometer. Stir until butter is melted. Milk mixture should not be higher than 110°F (43°C) before adding the yeast. Whisk in the yeast until it’s dissolved.

Add milk mixture and egg to dry ingredients. Mix to combine using a sturdy spoon or paddle attachment. Switch to dough hook attachment and knead in a stand mixer for about 3 minutes or by hand on a floured surface for 3-5 minutes. When ready, dough should feel wet but not stick to your hand. If dough is very too tacky, add 1-2 tablespoons more flour. If too dry, add 1-2 tablespoons water. Knead for another 30-60 seconds. Cover and let rise in a warm place for 60-90 minutes or until dough is doubled in size.

Grease a muffin pan and preheat oven to 350°F (175°C). Punch dough down gently. Then turn it out onto a floured surface. Press with your fingertips or use a rolling pin to shape it into a 12 x 16 inch (30 x 40 cm) rectangle.

Combine brown sugar and cinnamon (coating) in a small bowl. Brush dough with melted butter, then evenly sprinkle cinnamon sugar over the surface. Cut dough into (12) 4” squares.

Press each square into a greased metal muffin tin cavity, allowing the dough to come up the sides to form a cup. Leave corners hanging over the top or shape them along the walls of each cavity to create a smooth top.

Spoon 2-3 tablespoons of the pre-cooked apple pie filling into each dough cup. Press apples down gently to pre-settle before baking. It’s okay to heap apples up if you have enough as they will shrink in baking. Bake for 20-25 minutes, until the dough is golden and fully cooked through. While baking, make the frosting.

Beat cream cheese and butter in a medium bowl until smooth. Add powdered sugar and vanilla and beat until smooth. Thin with milk as needed for a thick drizzling consistency. Drizzle cream cheese frosting over the warm rolls, then finish with a drizzle of caramel sauce just before serving.