Using a large, sharp knife, pierce the spaghetti squash in several places.
Place the spaghetti squash in a glass baking dish and cook in the microwave on HIGH for about 12 minutes, turning the squash halfway through cooking.
Before handling, let the squash stand for 10 minutes. Cut 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. Keep warm.
Stack the spinach leaves in batches and thinly slice the leaves. Set aside.
Heat 2 teaspoons olive oil in a large nonstick skillet over medium-high heat. Add the onion and prosciutto, and cook until the onion is tender and the prosciutto is starting to become crispy. Add the garlic and saute for 30 seconds.
Add the spinach leaves and stir until the spinach is wilted, about 2 minutes.
Stir the spaghetti squash, Parmesan cheese, basil and 1 teaspoon olive oil into the prosciutto mixture and toss to combine.