Caramel-Apple Cupcakes with Cinnamon Cream Cheese Frosting

2/3 cup (11 tablespoons) unsalted butter, at room temp 2/3 cup granulated sugar 2/3 cup milk 1 teaspoon vanilla extract 1 large egg 1 1/3 cups all-purpose flour 2 teaspoons baking powder 1 1/2 teaspoons ground cinnamon 3/4 teaspoon ginger 3/4 teaspoon nutmeg 1/4 teaspoon kosher salt 2 apples, such as Gala or other baking apples, peeled, cored and chopped into small pieces (about 2 cups)