Preheat oven to 400°F. Slice squashes in half lengthwise. Scoop out seeds and brush flesh with 1 Tbsp. of the oil. Season with 1/2 tsp. salt and place flesh-down on a rimmed baking sheet lined with foil. Bake squash until fork-tender, about 35 to 45 minutes, depending on size.
Meanwhile, bring 1 1/4 cups water to a boil. Add cashews to water and remove from heat. Let stand 20 minutes.
Transfer cashews and soaking water to a blender. Add sun-dried tomatoes, nutritional yeast, lemon juice, 2 Tbsp. of the olive oil, and 1/2 tsp. salt; blend until smooth. Stir in black pepper and side aside.
Heat 1 Tbsp. oil in a large skillet over medium heat. Add mushrooms and shallots; cook 6 to 7 minutes, stirring occasionally, until mushrooms are golden. Stir in spinach and garlic; cook 2 minutes, stirring frequently, until spinach is wilted. Season with remaining 1/4 tsp. salt and stir in basil. Add vodka sauce to pan and stir to coat veggies; cook 1 minute to warm through.
To assemble, divide vodka sauce and veggie mixture evenly between squash boats. Garnish with additional fresh basil, if desired.