Combine flour, cheese, butter, corn starch, thyme and cayenne pepper in a food processor. Pulse until mixture resembles coarse oatmeal. Add sour cream, a spoonful at a time, pulsing until mixture is combined. Remove from food processor.
Knead 2 to 3 times forming dough into a ball. Divide the dough in half. Shape each half into a flat log, about 2-inches wide and 1/2-inch thick. Wrap logs in plastic wrap.
Refrigerate for 2 hours or overnight.
Brush the top of each log with milk and sprinkle with black pepper. Slice the dough at 1/4-inch intervals and place on baking sheets.
Bake in preheated 325°F oven for 25 to 30 minutes until golden brown. Cool on a wire rack. Delicious served with Beer Cheese Soup.