Just before serving, cut 10 rounds from frozen ice cream, using a 2 1/2-inch cutter, and place each round between 2 cookies.
Pistachio Ice-Cream Sandwiches: Prepare recipe as directed, substituting 2 pt. pistachio gelato (such as Talenti Sicilian Pistachio Gelato) for strawberry ice cream and 15 drops green liquid food coloring and 3 drops yellow liquid food coloring for red food coloring.
Mango Ice-Cream Sandwiches: Prepare recipe as directed, substituting 2 pt. mango sorbet for strawberry ice cream, reducing red liquid food coloring to 5 drops, and adding 20 drops yellow liquid food coloring.
Beat egg whites with an electric mixer on medium speed until foamy, about 1 minute. Gradually add granulated sugar and cream of tartar, beating until mixture is glossy and holds soft peaks, about 3 minutes.
Add food coloring and almond meal mixture to egg white mixture. Gently fold until batter is smooth and somewhat fluid, about 4 minutes, repeatedly pressing batter against sides of bowl in long, wide strokes.
Transfer batter to a piping bag fitted with a 1/4-inch round tip, and pipe rounds over pre-traced circles on parchment paper in prepared baking sheets. Firmly tap baking sheets on the counter 4 times to release any air bubbles. Set aside until tops of cookies are dry, about 30 minutes.
Preheat oven to 300°F with rack in the bottom third of the oven. Bake cookies, 1 baking sheet at a time, on bottom oven rack of preheated oven until edges of cookies can be gently lifted from parchment, 20 to 22 minutes. Cool completely on pan on a wire rack, about 20 minutes.