Banana Stuffed French Toast

Name: Banana-Stuffed French Toast
Ingredients: 1 firm, ripe banana; 3/4 cup half-and-half; 2 large eggs; 1 teaspoon vanilla; 1/4 teaspoon cinnamon; 1/4 teaspoon freshly grated nutmeg; four 1-inch-thick slices day-old challah or brioche; 2 tablespoons unsalted butter; confectioners' sugar for dusting; Accompaniment: warm maple syrup