Place the egg whites and sugar in a mixing bowl, and set over a pot of simmering water.
Cook, whisking continuously, until the mixture is hot, opaque, and the sugar is completely dissolved (it should not feel gritty between your fingers), about 5 minutes.
Whip the mixture on high speed, until stiff peaks form and it has completely cooled. (There should be no hint of warmth remaining when you place your hand on the side of the mixing bowl. Place the bowl and whip attachment in the refrigerator for 10-20 minutes, if needed.)
Add the butter, a tablespoon at a time, whipping well after each addition. (If it begins to look curdled, continue to beat until it comes back together, before adding the remaining butter.)
Stir in the peanut butter and chopped cookies, and pipe onto the cooled cupcakes.
Turn the frosted cupcakes upside-down into the melted chocolate, allowing the excess to drip away before inverting and allowing to harden.
Top with half a Peanut Butter Tagalong/Patty, for garnish.