Preheat oven to 400 degrees F. Place squash halves, cut side down, on a rimmed baking sheet. Bake until tender, 40 to 50 minutes.
Meanwhile, heat a large skillet over medium heat and add 1 tablespoon of EVOO. Add mushrooms, tomatoes, ¼ teaspoon salt, and spice blend. Cook, stirring until the mushrooms are soft and starting to brown, 5 to 6 minutes. Remove from heat.
For the pesto: combine basil, the remaining 3 tablespoons oil, garlic, cashews, lemon juice, nutritional yeast, the remaining ¼ teaspoon salt and pepper in a food processor. Process until mostly smooth.
Use a fork to scrape the squash flesh from the shells into a colander. Press lightly on the flesh to remove some of the liquid. Divide the squash among four plates. Top each serving with mushroom mixture and a dollop of basil pesto.