Make the shortcakes: Line a rimmed baking sheet with parchment paper. Whisk the all-purpose flour, almond flour, cocoa powder, granulated sugar, baking powder and salt in a large bowl until combined. Work in the butter with your fingers until it is in pea-size pieces, then stir in the chopped chocolate. Whisk the heavy cream and egg in a small bowl, then add to the flour mixture and stir until combined. (The dough will be slightly sticky.)
Scoop 6 balls of dough (about 1/3 cup each) onto the prepared baking sheet using a large ice cream scoop or a measuring cup, spacing the dough 2 to 3 inches apart. Freeze until firm, about 30 minutes.
Preheat the oven to 375 degrees F. Lightly brush each ball of dough with melted butter and sprinkle with turbinado sugar. Bake until the edges are firm and a toothpick inserted into the centers comes out clean, 25 to 30 minutes. Let cool 10 minutes on the baking sheet, then transfer to a rack to cool completely.
Meanwhile, make the filling: Toss the cherries with 1/3 cup granulated sugar, the cornstarch, almond extract and water in a medium saucepan; let sit 30 minutes. Cook over medium heat until the juices are bubbling and syrupy, 10 to 15 minutes. Transfer to a bowl and stir in the amaretto. Let cool to room temperature, at least 2 hours.
Beat the heavy cream and the remaining 1/4 cup granulated sugar in a medium bowl with a mixer on medium-high speed until stiff peaks form. Whisk the mascarpone to loosen, then beat into the whipped cream until medium peaks form. Refrigerate until ready to use.
Split each shortcake and fill with the whipped cream and cherries.