Preheat oven to 400 degrees. Spray 2 baking sheets lightly with nonstick spray. You can also use parchment paper instead of the spray.
Place pecans in a food processor and process until finely ground.
With an electric mixer on medium speed, beat egg whites and cream of tartar in a large bowl until soft peaks form. Add granulated sugar, one tablespoon at a time, beating until egg whites form stiff, glossy peaks. Beat in cocoa powder and vanilla. With rubber spatula, gently fold in pecans.
Transfer egg white mixture to a large zip-close bag with one corner snipped off. Pipe 72 mounds (each about 1 rounded tablespoon) onto baking sheets. Place in oven and reduce heat to 250 degrees. Bake until meringues are dried and crisped, about 1 hour. Remove from oven and cool completely on baking sheets.
Place the meringues in an airtight container and store at room temperature up to 3 weeks.