Step 1Heat the oven to 350 degrees. In a medium pot, bring the 2 quarts of water to a boil, then add 2 teaspoons salt and the squash. Reduce the heat and simmer the squash, covered, until they are just tender when pierced with a knife, about 8 to 10 minutes (timing will vary depending on the size and age of the squash). Drain the squash and chill in a bowl of ice water until cool to the touch.
Step 2Halve each squash lengthwise, and scoop out the flesh in the center with a spoon, making sure to leave enough flesh near the shell so the shells can be stuffed. Place the scooped flesh in a strainer and set aside to drain for at least 10 minutes to drain excess liquid.
Step 3While the squash is draining, heat a medium saute pan over medium-high heat. Add the oil, then the onion and garlic and saute until the onion is softened and translucent, 3 to 4 minutes. Stir in the mushrooms and continue to cook until they are tender and lightly browned, another 5 to 6 minutes. Stir in the drained squash flesh (don't worry if it is still moist, it will not be completely dry) and stir well to combine, scraping any browned bits from the bottom of the pan. Remove from heat and set the squash filling aside to cool slightly.
Step 4In a medium bowl, combine the squash filling, queso fresco and one-fourth cup parsley. Stir well and season with a generous one-fourth teaspoon salt and several grinds of pepper.
Step 5Divide the filling into the squash shells. Place the shells in a large baking dish or on a rimmed baking sheet and bake until hot and lightly browned in spots, 25 to 35 minutes depending on the size of the squash. Sprinkle with the remaining 1 teaspoon of parsley and serve.