Cut the chorizo into small pieces and add to a cold pan. Heat over medium-high heat until the chorizo is browned and crispy and has released lots of fat. Stir the chorizo from time to time making sure it doesn't stick to the pan and it's browned and crispy on all sides. Transfer chorizo to a plate lined with paper towels to drain excess fat*. Clean the pan with paper towels reserving about 1 teaspoon of fat.
In the meantime, beat the eggs with milk, until smooth, season with salt and pepper to taste.
Add the eggs to the pan and cook, stirring from time to time. When the eggs are half set, add the chorizo back to the pan, stir until just combined and the eggs are set. The eggs should be soft, creamy, and not dry.
Take the pan off the heat and immediately and transfer the scrambled eggs to a plate (so they won't overcook in the pan).
Clean the pan with paper towels and warm up the tortillas in the pan, on both sides until warm and slightly brown (I like to add a small amount of oil and cook the tortillas with oil, this is optional).