Preheat the oven to 350°F. Line a muffin tin with paper liners, or grease it well.
Make the topping first: in a bowl, combine the sugar, flour, and salt. Add the cold butter and massage it into the dry ingredients with your hands or a pastry blender until you have coarse, clumpy crumbs. Refrigerate while you make the batter so the butter stays cold.
Toss the diced apple (cut into small pieces, about 1/4 inch, so they fit nicely in a cupcake) with the brown sugar, cinnamon, and 1/4 cup white sugar. The sugar will draw out the juice and form a syrup. Set aside while you make the batter.
Using a hand mixer, or a stand mixer with the paddle attachment, cream the butter with the white and brown sugars.
Beat in the eggs, then the buttermilk, until just combined.
Add the flour, baking soda, baking powder, and salt. Mix only until combined. Do not overmix.
Gently fold in the apple filling, including all the syrup.
Divide the batter among the prepared cups, filling each about 2/3 full.
Sprinkle a generous spoonful of streusel over each cupcake. This will melt into cupcake and give you the brown sugar pockets.
Bake for about 18-20 minutes, until a toothpick comes out clean and the topping is golden brown.
Cool in the pan for 5 minutes, then move to a wire rack.
Top with cream cheese frosting, or just eat plain!