Heat the oil or butter in a frying pan over medium heat until it shimmers and starts to sizzle.
Add the diced chorizo to the pan and cook, stirring occasionally, until it develops a deep golden crust and is fragrant, about 4-5 minutes.
Sprinkle the smoked paprika over the cooked chorizo and stir to coat the sausage evenly, releasing a smoky aroma.
Crack the eggs directly into the pan, around the chorizo, and gently scramble them with a spatula, allowing the eggs to start setting and get fluffy, about 2-3 minutes.
Continue to cook, gently stirring, until the eggs are just cooked through but still soft, and the chorizo is well integrated within the scramble.
Remove the mixture from heat and transfer onto a warm plate or directly onto a toasted wrap to serve.