Preheat your oven to 350°F (175°C) and line a cupcake pan with paper liners.

In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-5 minutes. Add eggs one at a time and mix in vanilla.

In another bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Gradually add to the wet mixture, alternating with milk.

Fold in the grated carrots gently with a spatula.

Spoon the batter into the cupcake liners, filling each about two-thirds full.

Bake for 18-20 minutes and check for doneness with a toothpick. Allow to cool in the pan for 5 minutes before transferring to a wire rack.

Mix cream cheese, powdered sugar, and vanilla until smooth for the filling.

In a small bowl, mix flour, brown sugar, melted butter, and cinnamon to create the crumble topping.

Cut a hole in the center of each cooled cupcake, fill with cream cheese filling using a piping bag.

Whisk together powdered sugar, milk, and vanilla for the glaze and drizzle over the cupcakes.

Sprinkle the crumble topping over each cupcake while the glaze is still wet.