Preheat oven to 250°F (130°C). Using a permanent marker, trace 6 (6-inch) circles ¾ inch apart on 2 sheets of nonstick parchment paper; turn parchment over, and place on 2 rimmed baking sheets.

In the bowl of a stand mixer fitted with the whisk attachment, beat egg whites, cream of tartar, and salt at medium-high speed until foamy. Add sugar in a slow, steady stream, beating until glossy, stiff peaks form and stopping to scrape sides of bowl. Gently fold in one-third of finely chopped peanuts and vanilla bean paste just until combined; gently fold in remaining finely chopped peanuts in two additions just until combined.

Working quickly, spoon meringue mixture into a pastry bag fitted with a ½-inch round piping tip (Wilton No. 2A). Starting from outer edge of drawn circles and moving inward, quickly pipe meringue mixture onto prepared parchment. Using a small offset spatula, gently smooth, fill, and level meringue rounds where necessary.

Bake until golden, dry, and mostly firm to the touch (meringues will continue to firm as they cool), 2 to 3 hours (see Notes), rotating pans halfway through baking. Let cool completely on pans on wire racks.

Place a cooled meringue round on a serving plate. Using a small offset spatula, spread ¾ cup (126 grams) Coffee German Buttercream onto meringue round. Top with second meringue round; spread ¾ cup (126 grams) buttercream on top. Repeat procedure three times, and top with remaining meringue round, flat side down. Spread remaining buttercream on top and sides of stacked meringue rounds. Refrigerate for at least 30 minutes. Garnish with roughly chopped peanuts, if desired. Let stand at room temperature for 15 to 20 minutes before slicing and serving.