2 1/4 cups blanched whole almonds (about 12 ounces), plus 15 for garnishing
2/3 cup sugar
2 large egg whites, at room temperature
1/4 teaspoon salt
1/2 teaspoon pure almond extract
1/4 teaspoon pure vanilla extract
15 glacéed cherries
Arrange racks in upper and lower thirds of oven and preheat to 350°F. Lightly oil 2 large baking sheets, then line with parchment paper.
In food processor, combine 2 1/4 cups almonds and 1/3 cup sugar. Process until finely ground, scraping down sides once or twice. Set aside.
In electric mixer fitted with whisk attachment, beat egg whites and salt at high speed until soft peaks form. Reduce speed to medium and gradually sprinkle in remaining 1/3 cup sugar. Return speed to high and beat mixture until stiff, shiny peaks form. Gently fold in ground almond mixture and almond and vanilla extracts.
Roll mixture into 1-inch balls, place 2 inches apart on baking sheets, and flatten slightly. Top each with glacéed cherry or almond. Bake until cookies are golden, switching positions of pans halfway through, about 25 minutes. Cool on sheets 5 minutes, then transfer to racks to cool completely.
Cookies keep, wrapped, several days, or frozen, several weeks. Recrisp in warm oven.