In a medium bowl, cream together the butter, sugar, and vanilla. Beat in eggs, one at a time. Sift together the flour, baking powder, salt and nutmeg; gradually stir into creamed mixture. Cover and refrigerate until firm.
Preheat oven to 375 degrees F (190 degrees C).
Drop by heaping spoonfuls onto an unprepared cookie sheet. Bake for 6 to 8 minutes in the preheated oven. Cookies should be lightly browned.