In a medium bowl, beat the eggs with the salt and several grinds of pepper.

Heat a drizzle of olive oil in a nonstick skillet over medium heat. Add the scallions and spinach and cook until the spinach is just wilted, about 1 minute. Add the eggs and scramble until just set, about 1 minute. Remove from the pan and set aside.

Lay the tortillas flat on a clean work surface. Sprinkle half the cheese evenly over one half of each tortilla, leaving the other half bare. Evenly distribute the egg mixture and jalapeño slices over the cheese, then top with the remaining cheese. Fold the bare half of each tortilla over the fillings to create a half-moon shape.

Heat a dry cast iron skillet over medium-low heat. When hot, add two of the quesadillas and cook until the cheese is melted and the quesadillas are browned on both sides, 1 to 2 minutes per side. If the tortillas are browning faster than the cheese is melting, reduce the heat. Repeat with the remaining quesadillas.

Slice and serve with salsa, hot sauce, avocado, sour cream, and/or lime wedges for squeezing, as desired.