Preheat the oven to 350 degrees F (175 degrees C). Grease 3 mini-muffin tins or line cups with paper liners; this recipe makes about 66 mini cupcakes.

Melt 1 1/4 cups butter in a saucepan over low heat, add cocoa powder, and whisk until smooth. Stir in beer and vanilla extract. Remove from heat and allow to cool.

Combine flour, baking soda, baking powder, and salt and sift into in a large bowl. Mix in sugar. Add beer mixture and stir until thoroughly combined. Add eggs, stirring until well incorporated. Spoon batter into the prepared mini-muffin cups, filling each 3/4 full.

Bake in the preheated oven until tops spring back when lightly pressed, 10 to 11 minutes. Cool in the tins for 5 minutes. Transfer to a wire rack and let cool, about 20 minutes.

Beat 1 1/2 cups butter and confectioners' sugar in a bowl using an electric mixer. Add Irish cream liqueur, 1 tablespoon at a time, and beat until light, fluffy, and white in color, about 10 minutes. Top cooled cupcakes with frosting.