For the veggie Bolognese: Put the celery, carrot, onions, turnip and mushrooms in a food processor and pulse until coarsely chopped. This might have to be done in batches.
Heat the olive oil in a large high-sided skillet over medium-high heat. Add the chopped vegetables, 1 1/2 teaspoons salt and 1/2 teaspoon pepper and cook until tender but not mushy, about 10 minutes. Stir in the tomato paste, Worcestershire sauce, rosemary, oregano and red pepper flakes and cook for 5 minutes more.
For the spaghetti squash and mozzarella patties: Set a rack in the center of the oven and preheat it to 400 degrees F.
Cut each squash in half lengthwise and scoop out the seeds and fibers from the centers. Place on a baking sheet cut-side up and bake until easily pierced with a fork, about 40 minutes. Allow to cool slightly.
Once the squash is cool enough to handle, scoop out the spaghetti-like strands of the squash with a fork into a bowl. Once you fluff it back up you should have about 4 cups of squash. Place the squash in a bowl with the cooked spaghetti, Parmesan, 2 cups of the Veggie Bolognese. Reserve the remaining Bolognese for another use. Taste the mixture and season with up to 1 teaspoon salt.
Heat a large nonstick pan over medium heat. Lay 2 slices mozzarella in the pan side-by-side and top with one-eighth of the spaghetti squash mixture. Cook until the mozzarella is golden brown, about 3 minutes. Flip and cook until the pasta is crispy around the edges and warmed through, 2 to 3 additional minutes. Remove to a baking sheet. Repeat this process with the remaining mozzarella and spaghetti squash mixture.
For the butter-free garlic bread: Set a rack in the upper third of the oven and preheat the oven on the broiler setting.
Heat a small saute pan set over medium heat and spray with the cooking spray. Add the garlic and cook until softened, 3 to 5 minutes. Remove the pan from the heat and cool slightly.
Whisk together the Greek yogurt, thyme, cayenne pepper, 1/2 teaspoon salt and cooked garlic in a medium mixing bowl. Spread one-quarter of the mixture on the cut side of 1 piece of the halved bread. Top with one-quarter of the Parmesan. Repeat this process with the remaining bread and Parmesan. Place the bread in a single layer on a large baking sheet and cook under the broiler until the yogurt mixture and cheese are lightly browned and the bread is crisp, 5 to 7 minutes.
Cut each piece of bread in half crosswise to make 8 bread pieces total.
For the crispy pancetta: Heat a medium saute pan over medium heat and add the diced pancetta. Cook, stirring occasionally, until most of the fat has rendered and the pancetta is crispy, about 20 minutes. Drain any excess fat on a plate lined with paper towels.
For the sandwiches: Lay 1 piece of butter-free garlic bread down on a clean work surface. Top with 1 spaghetti squash and mozzarella patty, 3 tablespoons hot marinara sauce and a sprinkle of the crispy pancetta and garnish with the basil leaves.