How to Make It
Bring a large pot of salted water to a boil over high heat. Add pasta and cook until al dente, about 7 minutes or as package label directs. Drain, reserving 1/2 cup cooking liquid.
Warm oil in a large, deep skillet over medium heat. Add onion, sprinkle lightly with salt and pepper and sauté until translucent. Stir in mushrooms and cook, stirring occasionally, until they give up their liquid, about 5 minutes. Mix in ham and cook until warmed through, stirring once or twice, 1 to 2 minutes. Add ham mixture, Cheddar and basil to pot with pasta. Toss to combine, moistening with cooking liquid if necessary. Taste, season with salt and pepper, and serve.