Brush large nonstick skillet with olive or vegetable oil. Char tortillas over gas flame or directly on electric burner until blackened in spots, turning with tongs. Arrange tortillas in single layer in skillet. Sprinkle each tortilla with 1/4 cup grated cheese and set aside.
Whisk eggs and 2 tablespoons cilantro in medium bowl.
Season with salt and pepper.
Sauté chorizo sausage in heavy medium nonstick skillet over medium-high heat until cooked through, breaking up with back of spoon, about 5 minutes.
Add green onions and sauté 2 minutes.
Add egg mixture and stir until very softly set, about 1 minute.
Remove egg mixture from heat.
Cook tortillas in skillet over high heat until beginning to crisp on bottom, but still soft and pliable, about 1 minute. Divide egg mixture among tortillas and sprinkle with remaining 2 tablespoons cilantro. Fold each tortilla in half.