In a food processor, whirl powdered sugar and peanuts until nuts are very finely ground (no large nut pieces should be visible).
In a 3- to 4-quart pan over medium heat, bring 2 to 3 inches of water to a boil; adjust heat to maintain a very low simmer. In a large bowl or the bowl of a mixer, whisk sugar into egg whites. Set bowl over simmering water in pan (bottom of bowl should not touch water) and stir constantly until sugar is dissolved and mixture feels warm to the touch. Remove bowl from water and, with a mixer on high speed, whip egg white mixture until thick, stiff peaks form. Gently fold in nut mixture.
Spoon mixture into a pastry bag fitted with a 1/2-inch plain tip and, with the tip almost touching the parchment, pipe into flat, 2-inch circles about 1/8 inch thick, 1 inch apart, on two cooking parchment-lined 12- by 15-inch baking sheets.
Bake cookies in a 300° regular or convection oven until tops are shiny and dry and edges are cracked, about 15 minutes. Cool completely on baking sheets (about 1 1/4 hours), then remove cookies by gently lifting them up and peeling the parchment paper away from the bottoms.
Spread the flat side of each of half the cookies with about 1 teaspoon chocolate ganache. Top each with a second cookie, flat side toward filling.
Chocolate ganache: In a heatproof bowl set over (but not touching) barely simmering water in a pan, occasionally stir 6 ounces chopped bittersweet or semisweet chocolate, 2 tablespoons whipping cream, 1 tablespoon corn syrup, and 1 tablespoon butter until chocolate is melted and mixture is smooth. Remove from heat and let cool until thick but not firm, about 15 minutes. Makes about 1 1/4 cups.
Nutritional analysis per sandwich cookie.