Preheat oven to 400 degrees. Brush 30 cups of 2 mini-muffin tins with butter, and dust lightly with flour.
Melt butter in a medium skillet over medium-high heat. When it begins to sputter, reduce heat to medium. Cook, swirling skillet occasionally, until butter has lightly browned. Skim foam from top, and remove skillet from heat.
Whisk together flour, ground almonds, sugar, and salt in a bowl. Add egg whites, and whisk until smooth. Stir in kirsch. Pour in butter, leaving any dark-brown sediment in skillet, and whisk to combine. Let stand for 20 minutes.
Ladle 1 tablespoon batter into each buttered muffin cup, filling about halfway. Push a cherry into each, keeping stem end up. With a small spoon, smooth batter over cherries to cover. Bake until a toothpick comes out clean and cakes are golden brown, 12 to 15 minutes. Let cool 10 minutes. Run a knife around edges to loosen, and unmold. Cakes can be stored in airtight containers at room temperature overnight.