1. Make cupcakes: Preheat oven to 350ºF. Grease a 12-cup muffin tin and 4 cups of another tin, or line with paper or foil liners. (Pour 2 Tbsp. water into each empty cup.)
2. In a bowl, sift flour, baking powder, baking soda and salt. In a large bowl, using an electric mixer on medium speed, beat butter and sugar until light, about 3 minutes. Beat in eggs, one at a time. Beat in banana, yogurt and vanilla. Stir in flour mixture until just combined. Divide batter among muffin cups, filling each about 2/3 full. Bake until a toothpick inserted in a cupcake comes out clean, 15 to 20 minutes. Let cool in tins on a wire rack for about 15 minutes, then remove from tins to racks; let stand until cooled completely.
3. Make frosting: In a heatproof bowl set over a pan of just-simmering water, melt chocolate. Let cool to room temperature. In a bowl, using an electric mixer on medium speed, beat butter and sugar until light, about 3 minutes. Beat in milk, vanilla and chocolate until smooth.
4. Spread frosting on cupcakes. Garnish with sprinkles, if desired, and serve.