To begin, preheat your oven to 350 and line two muffin tins with 15 cupcake liners.
In a mixing bowl, add your dry ingredients (flour, cocoa powder, baking powder, salt, baking soda) and whisk them together thoroughly till there are no cocoa powder clumps. Alternatively, pour your cocoa powder into the bowl through a fine mesh strainer, to ensure there are no cocoa powder clumps.
In another mixing bowl, add your coconut oil and sugar and whisk them together. Next, add your eggs, milk and peppermint extract and whisk them together.
Pour your dry ingredients into your wet ingredients and whisk them together till everything is well incorporated. Your cupcake batter will seem very thin at this point (that's OK!).
Pour your cupcake batter into your cupcake liners, filling each cavity about 3/4 way full. Bake in the oven for 14-16 minutes, or till the top is spring to touch and a toothpick inserted comes out clean.
Let cool entirely before frosting.
In a large mixing bowl, add your butter and beat with a hand mixer till smooth and creamy. Add your powdered sugar, milk and peppermint extract and beat till smooth. If necessary, add a little more milk or a little more powdered sugar, till the frosting is the right texture.
Pipe on top of your cooled cupcakes. Add festive sprinkles or crushed up candy canes if you'd like!
Store these cupcakes on the counter for 1-2 days. You can also store them unfrosted in the fridge for up to a week, and frost them after removing them.