Preheat the oven to 375°F and line a muffin tin with 4 paper liners.
In a mixing bowl, stir together the 1 cup flour, granulated sugar, baking powder, cinnamon, and salt.
In a separate bowl, whisk the egg, milk, and melted butter until smooth.
Pour the wet mixture into the dry ingredients and stir gently until just combined.
Fold in the diced apple, then divide the batter evenly among the 4 liners.
In a small bowl, combine the oats, brown sugar, and 1 tablespoon flour. Cut in the cold butter until the mixture forms coarse crumbs.
Sprinkle the crumble evenly over each muffin.
Bake for 18 to 20 minutes until a toothpick inserted in the center comes out clean.
Let the muffins cool for 5 minutes, then drizzle the caramel sauce over the tops.