Preheat oven to 350°. Whisk together first 4 ingredients in a medium bowl until smooth. Stir in peanuts and vanilla. Drop by rounded tablespoonfuls 2 inches apart on lightly greased baking sheets.
Bake at 350° for 10 minutes or until puffed and lightly browned. Cool on pan on a wire rack 5 minutes. Remove from pan to wire rack, and cool 5 minutes. Serve warm or cool completely.