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.
Add flour, baking powder, baking soda, salt, and cinnamon. Stir in just until combined. Don't overmix.
Stir in carrots, raisins, and pecans just until incorporated.
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.