Prep. Crack the eggs into a medium bowl and whisk with the milk until well mixed.
Fire up. Bring the griddle grill to medium-high heat.
Cook. When the grill is hot, begin to cook the chorizo. As the chorizo cooks, chop it continually with a stiff spatula or metal scraper to promote even cooking and browning while it breaks into small pieces. Cover the chorizo and allow it to cook completely.
While the chorizo cooks, melt a couple of pats of butter on the griddle and sauté the pepper and onion until the peppers begin to wilt and the onions start to become translucent. Combine the chorizo and vegetables and spread them out evenly on the cooking surface.
If needed, add more butter to make sure the griddle is well greased before you pour the egg mixture into the chopped chorizo and veggies. Using a wide spatula or scraper, stir the egg mixture while it cooks and the eggs form curds. As the eggs solidify, scrape the eggs, chorizo and veggies aside and cover to keep warm.
Spread a thin coat of oil on the griddle and allow it to heat until shimmering. Place the tortillas in the oil and cook for about 2 minutes per side.
Uncover the chorizo mixture and add the cheese on top. Cook until the cheese melts.
Serve. Assemble the tacos by dividing the chorizo mixture into thirds and scooping it into a double-layered tortilla, then top with cheese.
