Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add apples, 1 pinch cinnamon, 1 pinch nutmeg, and 1 pinch cloves; cover and steam until tender, about 5 minutes.
Preheat oven to 325 degrees F (165 degrees C).
Mix graham cracker crumbs, butter, and 3 tablespoons white sugar together in a bowl; press into the bottom of a 9-inch springform pan.
Beat cream cheese, 1 cup white sugar, 2 tablespoons cinnamon, 1 teaspoon nutmeg, vanilla extract, and 1/4 teaspoon cloves together in a bowl using an electric mixer until smooth and creamy. Add eggs, 1 at a time, mixing on low speed just until blended.
Arrange a layer of apples onto the graham cracker crust, leaving a few for garnish. Pour cream cheese mixture over apples. Place pan in a larger baking dish and pour water onto the baking dish to create a water bath.
Bake in the preheated oven until the center is almost set, about 55 minutes. Cool on counter for 20 minutes before refrigerating until completely chilled, about 4 hours. Garnish with remaining steamed apples and drizzle caramel syrup over the top.