Preheat the oven to 350°F (175°C).

Combine the melted unsalted butter, room temperature unsalted butter, granulated sugar, and brown sugar in a mixing bowl. Mix until smooth and creamy, about 2-3 minutes.

Add the vanilla extract and large egg to the mixture. Blend well until fully incorporated.

Whisk together the all-purpose flour, kinako, salt, baking powder, and baking soda in a separate bowl.

Gradually mix the dry ingredients into the wet ingredients until just combined.

Fold in the coarsely chopped white chocolate and toasted white sesame seeds.

Scoop tablespoons of the dough onto a baking sheet lined with parchment paper, spacing them out. Top each mound with reserved doughnut coins.

Bake for about 20 minutes or until the edges are golden brown.

Cool the cookies on a wire rack before serving.