In a large pot of boiling, salted water, cook pasta until al dente, about 12 minutes.
Meanwhile, in a large skillet, heat oil and butter over medium-high heat. Add garlic Choose your mushroom. Shiitake, cremini and regular white mushrooms would work equally well in this dish. KITCHEN TIP and cook, stirring, for 1 minute. Add mushrooms and cook, stirring, until tender and golden, 4 to 5 minutes. Add tomatoes and beans and cook until heated through, 3 minutes.
Remove 1 1/2 cups pasta water and stir into mushroom-bean mixture. Drain pasta and return to pot. Add mushroom-bean mixture and basil to pot; toss well. Divide among 4 bowls and sprinkle Parmesan on top.