To the bowl of a food processor, add flour and cayenne pepper; pulse to combine. Add butter, and pulse until the mixture resembles coarse meal, 8 to 10 seconds.
Add cheese to the food processor; pulse until combined. Transfer the mixture to a large bowl.
Using a fork, stir in milk and Worcestershire sauce until well combined. Have ready several pieces of parchment paper.
Form mixture into two 1-inch-diameter logs, and wrap in parchment. Transfer the logs to the refrigerator, and chill until very firm, at least 1 hour.
Heat oven to 350 degrees. Line two baking sheets with parchment paper. Remove logs from refrigerator, and cut each one into 1/4-inch-thick rounds. Place the rounds on prepared baking sheets, spaced 1 inch apart.
Bake the shortbread until golden, about 12 minutes, rotating baking sheets between shelves halfway through baking.
Transfer shortbread to wire racks to cool. Bake remaining dough.
Dough can be stored in an airtight container for up to 2 days.