Fill a bowl with ice water. Bring a pot of salted water to a boil. Cut squash and zucchini in half lengthwise; place in boiling water. Bring back to a boil; cook until slightly softened, 5 minutes. Transfer squash to ice water. Cool for 2 minutes. Remove; pat dry.
Scrape out seeds and stringy pulp from each squash half, leaving a large cavity for stuffing. Arrange snugly in a large, lightly oiled ovenproof baking dish.
Warm 1 Tbsp. oil in a large skillet over medium-high heat. Add onions and cook, stirring often, until softened, about 3 minutes. Add turkey and cook, stirring to break up until crumbly, 2 to 3 minutes. Stir in tomatoes, broth and thyme. Increase heat to high and cook, stirring often, until turkey is thoroughly cooked and some of liquid has evaporated, 5 to 7 minutes. Season with salt and pepper.
Preheat oven to 425°F. Place equal amounts of filling in each squash half, piling it high in center. Mix bread crumbs with Parmesan, then sprinkle mixture over squash and drizzle with 2 Tbsp. olive oil. Bake until golden brown on top, about 20 minutes.