Place 2 of the flour tortillas on a work surface; evenly spread 1/4 cup of the cheese on top of each tortilla. Divide the steak evenly between the 2 tortillas. Sprinkle with jalapeno to taste. Spoon 1/4 cup of the salsa over each; top with the remaining cheese. Place another tortilla on top of each quesadilla; press down firmly with your hands to seal.
Heat a large skillet over high heat; add 1 1/2 teaspoon of the oil. Lower heat to medium; transfer one of the quesadillas to the pan. Cook until bottom tortilla is golden brown, about 2 minutes. Slide quesadilla to a dinner plate; invert another plate over it. Hold them together; flip plates to leave the quesadilla browned side up. Slide tortilla back into the hot pan to cook the other side until golden brown, about 2-3 minutes. Repeat with remaining quesadilla.