In a medium bowl, whisk together the flour, granulated sugar, brown sugar, cinnamon, and salt. Stir in the chopped pecans.
Slowly drizzle in the melted butter, stirring while it is being added to the dry ingredients. Without overworking the crumble, stir until the butter is just soaked in and the flour is no longer dry, 1 to 2 minutes. The crumble should be coarse and clumpy, about the size of a pea.
Cover the bowl with plastic wrap and place it in the freezer for about 20 minutes.
Muffins
Preheat the oven to 425°F (218°C). Line a standard muffin pan with cupcake liners or grease and lightly flour the muffin cups. Set aside.
In a medium bowl, whisk together the flour, baking powder, cinnamon, baking soda, and salt. Set this aside.
In a large bowl, beat the butter and sugar together until it becomes light and fluffy, 3 to 4 minutes. Beat in the egg, egg white, and vanilla.
In a glass measuring cup, whisk together the buttermilk and sour cream. Alternately, begin to add the flour mixture and the buttermilk mixture, beginning and ending with the flour mixture.
With a wooden spoon or spatula, fold in the chopped pecans.
Fill each of the prepared muffin cups with batter about three-quarters of the way full. Remove the crumble topping from the freezer and sprinkle the tops of the muffins with the crumble.
Bake the muffins for 10 to 12 minutes. Then, lower the oven temperature to 375°F (191°C) and bake the muffins for another 5 minutes, or until a toothpick inserted in the center comes out clean.
Let the muffins rest in their tin for about 10 minutes. Move the muffins to a wire cooling rack to finish cooling.
Powdered Sugar Icing
Whisk together the powdered sugar and milk until it is smooth and a bit runny. Drizzle the icing over the warm muffins before serving.
Notes
To store the muffins, keep them in an airtight container at room temperature for about 5 days.