Cook pasta according to package directions. Drain and set aside.

Heat 2 Tbsp. of oil in a large skillet. Add the onion and ham and cook until onion is translucent and ham is browned, about 4 minutes. Stir in garlic and cook 30 seconds more, until fragrant. Add in the tomatoes and sliced olives and cook another 1-2 minutes, until the tomatoes start to give up their juice.

Add the cooked pasta to the pan and toss to combine. Add more olive oil as needed to coat. Stir in Parmesan cheese, top with basil and serve.