Cook the pasta in a large pot of boiling, salted water to al dente. Drain. If the sauce is not quite ready, return it to the pot, and toss with a bit of olive oil to keep it from sticking.
Meanwhile, saute the ground beef. Heat enough vegetable oil to coat a large pan. Add the ground beef and spread it evenly across the pan. Cook until the bottom is browned, then flip. Continue to cook, stirring occasionally, until the beef is browned and no pink remains. Season to taste with salt and pepper, then remove to a plate.
In the same skillet, add the onions and peppers. Saute, stirring occasionally, until the onions and peppers have softened, about 7-9 minutes. Stir in the garlic and saute until fragrant, about 30 seconds. If there is a lot of excess oil, drain it off before proceeding.
Add the ground beef back to the pan, along with the pasta sauce, scraping up any browned bits from the bottom as you go. Bring the mixture to a simmer, then lower the heat and stir in the cream and cheddar cheese until melted.
Toss the cooked pasta shells with the sauce until thoroughly coated. Serve with grated Parmesan and basil or parsley, if desired.