Warm a large nonstick skillet over medium-low heat, add the chorizo, and cook for 5 minutes, breaking up the chorizo with a wooden spatula. Stir in the chopped onions and cook, stirring occasionally, until the sausage is cooked through and crispy, 5 to 6 minutes more.
Meanwhile, as the chorizo is being cooked, crack the eggs into a mixing bowl, season with salt, and whisk until well combined.
Remove the pan from the heat for a minute to allow it to cool slightly. Examine how much fat has been rendered from the sausage. Remove some from the pan if it is more than a tablespoon.
Return the pan to medium-low heat. Pour in the eggs and immediately swirl in small circles around the pan with a silicone spatula, without stopping, for about 30 seconds, or until the eggs appear slightly thickened, and small curds begin to form. Change from making circles to making long sweeps across the pan for about 20 seconds, or until you see larger, creamy curds.
Remove the pan from the heat and leave for a few seconds to finish cooking the eggs when they are softly set and slightly runny in places. Finish with one last stir and serve with the tortillas and a few lime wedges, as well as some cilantro leaves and cheese sprinkled on top.