Preheat oven to 375 F. Line 14 muffin tin cups with paper liners or grease with nonstick baking spray. Set aside.
In a large bowl, whisk together melted butter, brown sugar, egg, buttermilk, and vanilla until well-combined.
⅓ cup butter, 1 cup brown sugar, 1 large egg, ½ cup buttermilk, ½ teaspoon vanilla extract
Add flour, baking powder, baking soda, salt, and cinnamon. Stir in just until combined. Don't overmix.
1 ½ cups all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, ½ teaspoon salt, 1 teaspoon ground cinnamon
Stir in carrots, coconut, raisins, and pecans just until incorporated.
1 ½ cups grated carrots, ½ cup shredded coconut, ¼ cup golden raisins, ½ cup chopped pecans
Divide batter among muffin tins.
Bake about 18-25 minutes, or until a toothpick inserted in the center of a cupcake comes out clean.
Let cool in muffin tin for about 5-10 minutes and then remove to a wire rack to finish cooling.
Notes
Butter: Feel free to use salted or unsalted butter. If you prefer, you can use 1/4 cup of oil (like vegetable or melted coconut oil) in place of the melted butter.
Egg and buttermilk: It's important that the egg and buttermilk be at room temperature. Otherwise, they could cause the butter to re-solidify.
Coconut: I like to use sweetened shredded coconut. If you like less sweet muffins, you can use unsweetened shredded coconut.
Pecans: The pecans are optional. You can either omit them or replace them with additional raisins.