Preheat the oven to 400˚F (200˚C). Line a baking sheet with parchment paper.
To cut the squash, use a sharp knife to cut in half. If it is too tough, put in the microwave for 3 – 4 minutes until the squash is just soft enough to cut through. Remove the seeds with a spoon. Cut off the skin and cut the flesh into 1-inch cubes.
Transfer the squash cubes to the prepared baking sheet. Toss with 2 tablespoons olive oil. Season with salt and pepper. Combine well. Spread the squash in a single layer evenly. Bake in the oven for about 45 minutes until soften. Remove from oven to cool for 10 – 15 minutes.
In a large pan over medium heat, melt 1 tablespoon butter. Add onion and sauté for 3 – 4 minutes. Season with a pinch of salt. Reduce to medium-low heat, cook for about 35 – 40 minutes, stirring occasionally. Transfer to a small bowl.
In a medium pan, add the bacon pieces. Turn on the heat to medium. Cook until deep brown and crisp, stirring occasionally. Transfer to a plate lined with paper towels. Reserve bacon fat.
Transfer the squash to a food processor or blender, add 1/3 cup chicken broth and 1½ teaspoon bacon fat. Blend until smooth. If the puree is too thick, add more broth. If needed, adjust seasoning with more salt and pepper. Transfer the puree to a small bowl.
To assemble, place a tortilla on a working surface. Spread a thin layer (about 1/8-inch) of squash puree evenly on the tortilla. Layer with a little caramelized onion, bacon bits, 1-tablespoon of cortija cheese and a handful of mozzarella cheese. Cover with another tortilla. Repeat with the rest of the tortillas.
Heat a large griddle or skillet over medium-low heat. Add 1½ tablespoons of the vegetable oil (or reserved bacon fat), then add 2 of the mulitas and cook for about 3 minutes per side, or until they are golden brown and crisp on the outside and the cheese has melted. Repeat with the rest of the mulitas. Transfer to serving plates. Serve immediately.