Whisk together flour, baking powder, and salt.
Cream butter and granulated sugar in a bowl with a mixer on medium speed until light and fluffy, about ⏰ 5 minutes. Add egg and egg yolk, one at a time, beating just to combine after each. Beat in vanilla and almond extracts.
Add flour mixture; beat just until incorporated.
Divide dough in half. Return one half to mixer, add cherries and desired amount of red food color; mix to distribute. Shape dough into a disk, then wrap in plastic. Mix remaining dough half with pistachios and desired amount of green food color in a mixer; repeat shaping and wrapping. Chill doughs until firm enough to roll, about ⏰ 30 minutes.
Roll each dough between sheets of parchment into 8×10-inch rectangles.
Invert pistachio dough layer onto cherry layer; press lightly to adhere. Tightly roll up layers from long edge, jelly roll-style.
Roll dough log in pearl sugar, pressing to adhere; wrap in plastic and chill at least 2 hours.
Preheat oven to 350°. Line baking sheets with parchment. Slice log into ½-inch-thick slices; transfer to prepared baking sheets.
Bake cookies until edges are set, ⏰ 12–14 minutes; cool on baking sheets ⏰ 2 minutes, then transfer to a rack to cool completely.