- PREHEAT oven to 400°F.
- GRATE cheese using a food processor fitted with the shredding disc attachment; transfer to a medium bowl. Switch to blade attachment.
- SIFT flour, and lightly spoon into a measuring cup for 3 cups. Add salt, garlic powder, mustard, black pepper, and red pepper; sift again.
- ADD flour mixture and thyme to food processor; pulse 2 to 4 times to combine. Add cheese and butter; pulse until a dough ball forms.
- PIPE dough into long straight lines, about 1/2- to 3/4-inch apart, on ungreased baking sheets using a cookie press fitted with a ribbon disk. Gently pat down to ensure ribbons are lying flat on baking sheets.
- BAKE until lightly browned, 8 to 10 minutes.
- REMOVE from oven. Gently cut into 2.5-inch-long pieces using a small sharp knife. Loosen cheese straws from pans using a small offset spatula. Let cool completely.
- SERVE garnished with thyme, if desired. Store in an airtight container for up to 5 days.
KITCHEN TIP: To make ahead, let baked cheese straws cool completely. Place in a heavy-duty resealable plastic bag, pushing out as much air as possible; seal and freeze for up to 1 month. Remove from freezer and let stand at room temperature for at least 30 minutes before serving.