In a large pot cook spaghetti pasta with a teaspoon of oil in boiling salted water until al dente. Drain, leaving pasta moist.
Meanwhile, in a large skillet over medium heat saute the onions and garlic in 2 tablespoons of olive oil until soft and tender, about 3 or 4 minutes. Add the two cans of tuna and let cook on medium for 6 minutes. Add salt and pepper to taste, cooked pasta, and continue stirring. Turn burner to high heat, add remaining 2 tablespoons of olive oil and cook for 3 or 4 minutes.
Place the pasta in large serving bowl and toss with the fresh parsley and grated Parmesan cheese. Serve immediately.