Add the butter to a pan of boiling water.
Once the butter has melted, add the flour and whisk the mixture quickly with a wooden spoon until it comes away from the sides of the pan and has a smooth texture.
Allow the mixture to cool for five minutes then add the eggs, cheese and cayenne pepper, stirring well between each addition.
Heat the oil in a deep, heavy-bottomed saucepan until a breadcrumb sizzles and turns brown in 30 seconds when it is added (CAUTION: Hot oil can be dangerous, do not leave unattended).
Using a teaspoon dipped in vegetable oil, place spoonfuls of the mixture into the frying oil.
Fry each portion of the mixture for five minutes until it puffs up and turns golden in colour.
Remove the beignets from the oil with a slotted spoon, drain on kitchen paper and season with salt and freshly ground black pepper.
To serve, place the cheese beignets onto a clean plate and sprinkle the dill over the top.