Heat oven to 350 degrees. Melt 2 tablespoons butter in a large skillet over medium heat. Add the apples & 1/2 cup of the sugar; stir. Cook on medium-low heat for about 15 minutes, stirring occasionally, until the sugar is completely dissolved & golden brown. Stir in the milk & cinnamon. Cook for 3 minutes, stirring occasionally, and remove from the heat.
Microwave the remaining butter in a medium microwaveable bowl on high until melted, about 30 seconds or so. Add the graham cracker crumbs & 2 tablespoons of the remaining sugar. Mix well. Press into the bottoms of 8 paper lined muffin cups, adding about 1 tablespoon of the crumb mixture to each cup.
Beat the cream cheese, sour cream, & remaining sugar in a bowl with an electric mixer until blended. Add the egg; beat on low until just blended. Gently stir in half of the apples. Spoon the cheesecake mixture over the graham cracker crumb mini crusts.
Bake 20-22 minutes or until the centers are almost set. Cool completely.
Transfer the cheesecakes to a plate or another container & top with remaining cinnamon apples. Garnish with whipped cream and/or caramel, if desired.