In a standing mixer fitted with a whisk attachment, whip egg whites, cream of tartar, and granulated sugar to soft peaks at high speed. Add the powdered sugar and flour, a third at a time. Whip on high speed to stiff peaks. Fold in the peanuts.
Place batter in a piping bag, and pipe meringues into 2-inch long tubes onto a parchment paper lined sheet tray. Bake for 2 hours.
Hot Chocolate: Chocolate Caliente: Preheat oven to 325 degrees F.
Over a steam bath, melt the chocolate and the butter, stirring with a rubber spatula.
In an electric mixer cream the sugar and eggs and combine them with the melted chocolate. Add the cocoa and the vanilla extract. Mix until smooth and pudding-like.
Butter a mini muffin pan. Pour batter into muffin tin, filling the wells almost to the rim. Bake until center is set, about 25 minutes. Let puddings cool in the muffin pan and then turn out.
Place chocolate in a shallow bowl, heat for 45 seconds in a microwave, and serve with a dollop of whipped cream and a meringue.