Heat the vegetable oil in an 8-inch skillet. Add the onions and sauté for 2 minutes, until the onions are translucent. Add the shrimp and sauté for 3 to 5 minutes, until the shrimp is cooked throughout. Season with salt and pepper.
Heat a griddle on the stove. Place the tortilla on the hot griddle, and heat for 30 to 60 seconds. Flip the tortilla over, and then place a slice of the Pepper Jack cheese in the center of the tortilla. Spoon the half shrimp filling onto the cheese, then fold the quesadilla using a spatula. Grill the quesadilla on the griddle for 2 to 3 minutes on each side, until the cheese is melted.
Remove the quesadilla from the griddle, open carefully, and place half of the lettuce, onions and cucumbers inside. Prepare the remaining quesadilla in the same fashion. Serve hot with salsa on the side.