Beat butter at medium speed with an electric mixer until creamy; gradually add 1 cup sugar, beating until light and fluffy. Add eggs, 1 at a time, beating until blended after each addition.
Combine flour, baking powder, and salt; add to butter mixture, beating just until blended. Stir in fennel seeds and vanilla.
Divide dough into 2 portions; roll each portion on wax paper into a 12" log. Freeze 2 hours or until firm.
Cut each log into about 1/4" thick slices, using a sharp knife; place slices on ungreased baking sheets. Sprinkle cookies with desired sugar. Bake at 350° for 10 to 11 minutes or until edges are barely golden. Cool 1 minute on pans; remove to wire racks to cool.