1) In a medium bowl, whisk together the eggs and milk and season with salt and pepper.
2) Heat 1 tbsp of the oil in a medium skillet over medium heat. Add the chorizo and cook, stirring, until just beginning to brown, about 5 mins. Scoop the chorizo out of the skillet with a slotted spoon and transfer to a plate. Wipe the skillet out with a paper towel.
3) Return the skillet to medium to medium-low heat and heat the remaining 1 tbsp oil. Add the egg mixture and cook, stirring, about 3 mins. Add the chorizo and cook, stirring, about 2 to 4 mins more depending on the desired firmness of the eggs. Serve immediately.