In a medium mixing bowl, combine the softened butter and finely shredded sharp cheddar cheese. Use a sturdy spatula, wooden spoon, or hand mixer on low speed to blend until the mixture is well combined and almost paste-like. The cheese should be very finely shredded so it blends smoothly and bakes into visible cheesy texture instead of big clumps.
Sprinkle the cayenne pepper over the cheese mixture, then add the all-purpose flour. Stir and press the dough together with your spatula or hands until it forms a soft, thick dough that holds together when squeezed. It will seem dry at first; keep pressing and folding until there are no dry flour pockets.
If your kitchen is very cool and the dough is crumbly, knead it gently with clean hands for a minute