To prepare the quesadillas, heat 1 tablespoon of olive oil in a large skillet over medium-low heat. Add the onion, sprinkle lightly with sea salt and pepper, then stir to coat. Cover and cook for about 5 minutes, stirring occasionally until the onions have softened. Add the spinach and sprinkle with sea salt and pepper. Using tongs, turn the spinach to coat with the oil. Cover and continue cooking for about 5 minutes, using the tongs to turn the spinach until it’s tender to your preference. Arrange 3 of the tortillas on a cookie sheet. Sprinkle each tortilla evenly with about 2heaping tablespoons of the shredded cheese. Using tongs, arrange about one-third of the spinach mixture evenly over the cheese, first allowing as much of the juices as possible to drip back into the skillet as you lift out the spinach. Sprinkle about 2heaping tablespoons of the shredded cheese evenly over the spinach mixture. Repeat with the remaining 2 tortillas on the tray. Top each with a tortilla. Using your hands, gently press the tortillas together.
Transfer the tray of assembled quesadillas to the counter by the stove. Have a second cookie sheet handy so you can keep the finished quesadillas warm in the preheated oven while you cook the rest. Wash and dry the skillet to reuse it—you’ll appreciate having one less pan to wash after supper. Measure 1 of the remaining teaspoons of olive oil in a skillet over medium heat, then tilt the skillet to spread the oil around. Carefully transfer a quesadilla to the heated skillet. Carefully press the quesadillas together again to keep them together. Cover and cook for about 4-5 minutes, until the underside is golden brown. Using two large spatulas, carefully turn the quesadilla and cook the other side for about 2 minutes until it is golden brown.
Transfer the cooked quesadilla to the spare cookie sheet and set it in the preheated oven to keep it warm as you cook the remaining quesadillas. Add another teaspoon of the remaining olive oil, tilt the skillet to coat the bottom, and repeat the process until you've cooked all 3 quesadillas. Keep the quesadillas warm while you prepare the sauce.
To prepare the sauce, cut the avocado in half and remove the seed. Using a spoon, scoop the pulp into a bowl. Using a fork, mash it somewhat smooth. Add the sour cream, cilantro, lime juice, and a sprinkle of sea salt and pepper. Using the fork, mash the ingredients together. Taste for seasonings.
To serve, cut each quesadilla into quarters. Serve with the sauce on the side and encourage everyone to dip in.