Prepare the pan: Heat the oven to 350°F and line a standard muffin pan with paper liners.
Make the streusel: Combine flour, brown sugar, and cinnamon. Stir in melted butter until coarse crumbs form.
Mix the cake batter: Whisk the dry ingredients separately. Combine the egg, sugars, oil, and vanilla, then mix in the dry ingredients. Fold in carrots and pecans.
Prepare the filling: Beat softened cream cheese, sugar, egg, vanilla, and flour until smooth.
Layer: Add one tablespoon of carrot batter to each liner, followed by a heaping tablespoon of filling. Cover with more batter, filling cups three-quarters full.
Top and bake: Add streusel and press gently. Bake for 28 to 30 minutes, until the cake portion is set.
Cool and glaze: Cool briefly in the pan, transfer to a rack, and cool completely. Mix powdered sugar with milk and drizzle over the cakes.