Line a 13½x8½-inch rimmed baking sheet with plastic wrap. Spread ice cream in an even layer in prepared pan. Cover with plastic wrap, and freeze until firm, at least 1 hour, or up to overnight.
Using a permanent marker, draw 2½-inch circles 1 inch apart on 4 sheets of parchment paper. Place parchment, ink side down, on 4 rimmed baking sheets. (Alternatively, line 4 baking sheets with silicone macaron baking mats.)
In the work bowl of a food processor, pulse almond flour and confectioners’ sugar until fully combined. Transfer to a large bowl. Add 1 egg white (30 grams); fold until combined. (It may be difficult to stir at first but will come together.)
In the heatproof bowl of a stand mixer, whisk together granulated sugar and remaining 4 egg whites (120 grams) until frothy. Place bowl over a small saucepan of simmering water. Cook, whisking constantly, until sugar dissolves and an instant-read thermometer registers 140°F (60°C), about 2 minutes.
Carefully return bowl to stand mixer fitted with the whisk attachment. Beat at high speed until stiff peaks form, 3 to 4 minutes. Add butter extract, and beat until mixture is cooled and stiff peaks form, 4 to 5 minutes.
Add about 1 cup (80 grams) egg white mixture to flour mixture; stir vigorously until combined. Add remaining egg white mixture, and fold until mixture is ribbonlike. (Mixture should be thick and slowly but freely fall off the spatula in a “V” shape; when you drag the spatula through the batter, it should move like lava and slowly come back together. To get this consistency, it may require vigorous stirring to remove some air from the meringue and loosen the batter.)
Transfer batter to a pastry bag fitted with a medium round piping tip (Ateco #804). Holding piping tip perpendicular to pan, pipe batter within drawn circles on prepared pans, applying pressure and leaving tip stationary until batter just reaches drawn circle. Move and lift piping tip in a quick circular motion as you finish piping each macaron shell to prevent a point from forming on top.
Slam pans vigorously on counter 5 to 7 times to release air bubbles. Refill pastry bag with remaining batter, and repeat. Let batter stand at room temperature until a skin forms on top, 40 to 50 minutes. (This time frame could vary depending on the humidity of your kitchen. Batter should feel dry to the touch and should not stick to your finger.)
Preheat oven to 300°F (150°C).
Bake until shells are firm but have a slight wobble to the touch, 15 to 18 minutes, rotating pans halfway through baking. Let cool completely on pans on wire racks.
Line a rimmed baking sheet with parchment paper.
To assemble: Using a 2½-inch round cutter, cut rounds from ice cream. Place on flat side of half of macaron shells. Top with remaining macaron shells, flat side down. Dip macarons halfway into melted chocolate, letting excess drip off; sprinkle with peanuts. Place on prepared pan.
Freeze until firm before serving, about 1 hour. Freeze in an airtight container for up to 5 days.