Preheat the oven to 375°F (190°C). Line a standard 12-cup muffin pan with paper liners and lightly grease the tops of the pan. In a small bowl, combine the flour, brown sugar, and cinnamon for the crumble topping, then cut in the cold butter until coarse crumbs form. Refrigerate while preparing the batter.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon. In a separate large bowl, whisk the melted butter, granulated sugar, eggs, vanilla extract, sour cream, and milk until smooth and well combined.
Gently fold the dry ingredients into the wet ingredients just until combined, then carefully stir in the diced apples. Avoid overmixing to keep the muffins soft and tender.
Divide the batter evenly among the prepared muffin cups, filling each about three-quarters full. Generously sprinkle the chilled crumble topping over each muffin, pressing it lightly so it adheres.
Bake for 20 to 22 minutes, or until the tops are golden and a toothpick inserted into the center comes out clean or with a few moist crumbs. Let the muffins cool in the pan for 5 minutes before transferring them to a wire rack to cool slightly. Serve warm or at room temperature.
