How to Make It
Heat the oven to 350°F. Line a standard 12-cup muffin tin with paper liners. Combine the flour, cinnamon, ginger, baking powder, and salt in a medium bowl.
Combine the buttermilk, vegetable oil, sugar, egg, egg yolks, vanilla, and carrot in a large bowl. Fold the dry ingredients into the wet ingredients.
Divide the batter evenly between the liners. Bake until a toothpick inserted into the center of the cupcakes come out with just a few moist crumbs, 22 to 25 minutes. Transfer the cupcakes to a rack to cool completely.
Prepare the frosting: Add the butter to a skillet over medium-high heat and cook, stirring constantly, until golden, 4 to 5 minutes. Transfer to a bowl and let cool to room temperature.
Add the cream cheese to the butter and beat with an electric mixer until smooth. Add the confectioners’ sugar and salt and beat again until smooth. Top the cupcakes with the frosting and toasted coconut, if desired.