Beat first 5 ingredients at medium speed with a heavy-duty stand mixer until blended. Gradually add flour, beating just until combined.
Use a cookie press with a star-shaped disk to shape mixture into long ribbons, following manufacturer's instructions, on parchment paper-lined baking sheets. Cut ribbons into 2-inch pieces.
Bake at 350° for 12 minutes or until lightly browned. Remove to wire racks to cool.
Cheese Wafers: Combine ingredients as directed; chill dough 2 hours. Shape dough into 4 (8-inch-long) logs; wrap each in plastic wrap, and chill 8 hours. Cut each log into 1/4-inch-thick slices; place on parchment paper-lined baking sheets. Bake at 350° for 13 to 15 minutes or until lightly browned. Remove to wire racks to cool. Store in an airtight container 1 week.
If you don't have a heavy-duty stand mixer, you can use a handheld mixer. Just divide the ingredients in half, and work with two batches.