Stir together first 5 ingredients in a medium bowl, using a wooden spoon. Stir in peanuts.
Drop cookie dough by rounded tablespoonfuls onto a parchment paper-lined baking sheet.
Bake at 350° for 12 minutes or until puffed and golden. (Cookies will be soft in the center.) Cool cookies on baking sheet 5 minutes. Remove to a wire rack.