Preheat the oven to 400 degrees F. Grease the muffin cups or line them with paper liners
For the topping. combine the 1/2 cup flour, 1/4 cup brown sugar, 1/4 granulated sugar, and cinnamon. Add the butter and cut it in until well combined. Set aside
In a large bowl combine the 1 1/2 cup flour, 1/2 cup brown sugar, 1/4 cup granulated sugar, baking powder, baking salt, 1 teaspoon cinnamon, ginger, nutmeg, cloves, and chopped pecans.
In another bowl beat together the egg, buttermilk, oil, vanilla, and carrots.
Add the wet ingredients to the dry and mix until combined.
Divide the batter between the muffin cups filling each cup about 2/3 full.
Divide the topping, sprinkling over the top of the batter.
Place the muffins in the oven and bake for 15 to 17 minutes.
Remove from the oven and set on a cooling rack for a few minutes. Then remove the muffins from the tin and set them on the cooling rack and cool completely.