In a large pot of salted boiling water, cook the pasta until al dente. Drain and oil lightly. Set aside.
In a large skillet or in the same pot, heat the oil with the red pepper flakes. Add the onions and cook until slightly tender. Add the mushrooms and garlic. Cook until the mushrooms begin to release their juices.
Add the tomatoes and wine. Simmer for 1 to 2 minutes. Add the broth and cooked pasta. Stir well to heat throughout. Adjust the seasoning. Just before serving, add the basil. Garnish with Parmesan shavings and serve.
Parmesan shavings are easy to make yourself, especially if you follow this one simple rule: the cheese should be at room temperature, not cold. With experience, you’ll recognize the right moment to gently shave the cheese with a vegetable peeler.