1 stick plus 1 tablespoon unsalted butter
3/4 cup (packed) plus 3 tablespoons light brown sugar
2 large eggs
1 1-inch piece of fresh ginger root (peeled and finely grated)
1/2 cup finely minced crystallized ginger (divided)
1 cup unbleached all-purpose flour
1/2 teaspoon baking powder
1 teaspoon ground ginger
1/4 teaspoon salt
6 ripe Fuyu persimmons (peeled and sliced 1/4-inch thick)
1 tablespoon confectioner's sugar