1. In a large bowl, whisk the eggs and milk for an omelette. When they are well frothy, season with salt and pepper.
2. In a non-stick pan, melt 1 tablespoon of butter. Add the chorizo, and cook for 2 minutes.
3. In a non-stick pan, melt the butter. Pour in the beaten eggs and cook the omelette over medium heat, bringing the eggs from the sides to the center so that the mixture cooks evenly.
4. Sprinkle with paprika and serve hot.