Preheat your oven to 350°F (175°C). Generously grease a 12-cup muffin tin with cooking spray or butter.
In a small bowl, combine the melted butter and brown sugar until you reach a thick, smooth paste. Divide this mixture evenly among the muffin cups, using approximately 1 tablespoon per cup.
Core and peel the apples, then dice them into small, uniform ¼-inch pieces. Toss the diced apples with cinnamon and a pinch of salt before arranging them evenly over the caramel mixture, pressing down lightly.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy, about 2-3 minutes.
Beat in the eggs one at a time, then stir in the vanilla extract, sour cream, and milk.
Gently fold the dry ingredients into the wet mixture until just combined. Do not overmix.
Carefully spoon the batter over the apple and caramel layer in each muffin cup, filling each about ¾ full. Use the back of a spoon to gently spread the batter to the edges.
Bake for 22-25 minutes, or until the tops are golden brown and a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for exactly 10 minutes. Run a knife around the edges of each muffin, then place a large baking sheet or cutting board over the muffin tin and carefully flip everything over in one swift motion.