HEAT oven to 375°F. Generously COAT 2 madeleine pans (12 cups per pan) with cooking spray; dust with flour, tapping out excess.
BEAT eggs and sugar in mixer bowl with whisk attachment on high speed until light and fluffy, 5 to 10 minutes. BEAT IN almond extract and vanilla.
FOLD IN flour, 1/3 at a time. FOLD IN butter, 1/3 at a time. FOLD IN cherries. SPOON 2 Tbsp. batter into each madeleine cup.
BAKE in 375°F oven until cookies pull away from sides of cups and wooden pick inserted in center comes out clean, 8 to 10 minutes. LOOSEN cookies with tip of knife if necessary. REMOVE from pans immediately; cool completely on wire racks.
Madeleines, buttery French teacakes, have a delightful spongy texture. They are traditionally baked in pans with cups shaped like elongated scallop shells. The pans usually have 12 cups each. If you only have 1 pan, bake half the batter. Quickly clean the molds, let cool, then grease and flour again before baking remaining batter.
Pan alternate: Mini muffin pans (1-3/4-inch diameter) can be substituted for madeleine pans. Use 1 1/2 Tbsp. batter for each mini muffin and increase baking time to 10 to 12 minutes. Because these cups hold less batter, you will need 3 pans. Or, plan to bake batter in 3 batches.