Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Spread the almonds on a rimmed baking sheet and bake until slightly darkened, about 10 minutes; let cool completely. Transfer to a food processor and pulse until finely ground. Add the flour and pulse to combine.
Beat the butter in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Add 1/2 cup confectioners' sugar, the vanilla and almond extracts, and salt and beat until combined. Reduce the mixer speed to low; add the flour mixture and beat until just incorporated. Cover and refrigerate until slightly firm, about 30 minutes.
Meanwhile, combine the dried cherries, amaretto and 1 tablespoon water in a small microwave-safe bowl and microwave 30 seconds; set aside until the cherries are plump, about 20 minutes.
Scoop out a tablespoonful of dough, press a dried cherry into the center, then shape the dough into a ball, enclosing the cherry. Repeat with the remaining dough and cherries and arrange about 1 inch apart on 2 ungreased baking sheets. Bake, switching the position of the pans halfway through, until lightly golden on the bottom, 15 to 20 minutes. Put the remaining 1 cup confectioners' sugar in a large shallow bowl. Let the cookies cool 5 minutes on the baking sheets, then carefully transfer to the bowl with the sugar and gently toss. Transfer to racks to cool completely, then toss in the sugar again.