Preheat oven to 375° (350° if using a glass baking dish). Make filling: Immerse a few peaches at a time in a saucepan of boiling water until skin loosens easily with a knife tip, 15 to 30 seconds. Peel fruit.
In a large bowl, combine brown sugar, cornstarch, and tapioca. Stir in lemon juice and bourbon. Cut peaches into 1/2-in.-wide wedges to make 6 1/2 cups. Stir peaches into bourbon mixture and let stand 15 to 20 minutes, stirring occasionally, for tapioca to begin to soften.
Meanwhile, make topping: Combine flour, baking powder, and salt in a bowl. In a food processor, whirl almond paste and granulated sugar to break up. Add butter; whirl until no lumps remain, scraping bowl. Add egg, milk, and flour mixture and pulse just until blended. Transfer to bowl used for flour.
Scrape fruit mixture into a 10-in. cast-iron skillet (2 in. deep) or an 8-in. square baking dish. Drop batter in 8 large spoonfuls over fruit and scatter all over with almonds.
Bake until topping is golden brown and filling is bubbling, about 40 minutes (50 minutes for a glass dish). Let cool on a rack at least 30 minutes.