Preheat the oven to 375°F (190°C).
In a mixing bowl, combine the flour, salt, and cayenne pepper.
In another bowl, cream the softened butter and shredded cheddar cheese until well blended.
Add the garlic powder, onion powder, and egg yolk to the cheese mixture, mixing until combined.
Gradually add the flour mixture to the cheese mixture, mixing until a dough forms.
If the dough is too dry, add cold water, one tablespoon at a time, until it comes together.
Roll out the dough on a lightly floured surface to about 1/4 inch thick.
Cut the dough into strips or desired shapes using a knife or cookie cutter.
Place the cheese straws on a baking sheet lined with parchment paper.
Bake in the preheated oven for 15-20 minutes or until golden brown.
Remove from the oven and let cool on a wire rack before serving.