In a large bowl, cream butter and sugar until light and fluffy. Add fennel seeds and salt. Add egg and beat to combine.
In a small bowl, stir together flour, cornmeal, and baking powder. Add these dry ingredients to butter mixture in 3 batches, mixing after each addition. Shape dough into a log, wrap in plastic wrap, and refrigerate at least 2 hours and up to 1 day.
Preheat oven to 375°. Break off small bits of dough and roll into balls about 1 1/2 in. wide. Arrange on parchment-lined baking sheets. Gently flatten each cookie using the bottom of a water glass (dip the glass in water to prevent sticking). Bake cookies for 8 minutes, or until golden brown and puffed. Transfer cookies to cooling racks.
Note: Nutritional analysis is per cookie.