In a medium bowl, combine cannellini beans, basil, oregano, 1 tablespoon olive oil, and white wine vinegar.
Using a large, sharp knife, pierce spaghetti squash in several places. Place the squash in a glass baking dish and cook in the microwave on high for about 15 minutes, turning the squash halfway through cooking. Before handling, let the squash stand for 10 minutes. Cut it in half lengthwise and scrape out the seeds and fibers. Using a fork, twist out strands of the spaghetti squash flesh and place in a large bowl.
Working in batches, stack the spinach leaves and cut across the leaves into ¼-inch wide strips.
In a large skillet, heat 2 tablespoons olive oil over medium heat. Add onion and garlic. Cook, stirring constantly for 1 minute. Add the sliced spinach and cook until the spinach is just wilted, 1 to 2 minutes. Add feta cheese and the cannellini bean mixture. Cook until heated through, 1 to 2 minutes. Season to taste with salt and pepper.
Add bean and spinach mixture to the spaghetti squash. Gently toss. Place the mixture on a serving platter and serve with finely grated Parmesan cheese.