Grind the black sesame seeds to a powder in either a blender, grinder, or with a mortar and pestle/suribachi.
1/2 cup toasted black sesame seeds
In a medium bowl, cream the butter and the sugar together.
1/3 cup granulated sugar, 1/4 cup unsalted butter
When nice and fluffy, add the egg, egg yolk, and vanilla, and beat again to combine.
1 egg, 1 egg yolk, 1/2 t vanilla extract
In a separate bowl, whisk the ground sesame seeds, flour, and baking powder together.
1/2 cup all purpose flour, 1 t baking powder, small pinch of salt
Add half of it to the butter mixture and stir to combine.
Next, add half of the milk, and mix.
1/4 cup whole milk
Finally, add the remaining flour, mix, and the remaining milk, and mix until fully combined. You want it to be fully combined, but you also want to be careful not to OVER mix it.
Divide among the 12 cupcake liners.
Bake for about 15-17 minutes or until a toothpick comes out clean, when inserted.
Cool on a wire rack.
In a medium sized mixing bowl, cream the butter and the powdered sugar together.
2 T unsalted butter, 1/4 cup powdered sugar
Add the vanilla, black sesame, and peanut butter, and mix to combine.
1/4 t vanilla, 1 T toasted black sesame seeds, 1 T peanut butter
Spread lightly over the cooled cupcakes. The frosting is meant to be a thin layer, and there will be just enough to frost all twelve cupcakes. If you really really like your frosting, consider doubling the recipe.
If you don't have a mortar and pestle, and you are grinding your seeds in a blender, add the seeds for the frosting and grind it all at once. Once ground, it will be about 1.5 T that you need to reserve for the frosting.