Preheat your oven to 400°F (200°C) or prepare your grill for medium-high heat.
In a large mixing bowl, combine the halved baby red potatoes, trimmed green beans, sliced bell peppers, and diced onion.
Add the sliced smoked sausage, dried oregano, dried parsley, garlic powder, paprika, salt, and pepper to the vegetables. Toss everything together until well coated.
Cut large sheets of aluminum foil (about 12 inches long). Divide the mixture evenly among the sheets, placing it in the center. Top each portion with cubed butter and a generous helping of shredded sharp cheddar cheese.
Fold the sides of the foil over the mixture, then fold the top and bottom to create a sealed packet. Ensure they are well sealed to trap the steam.
Place the foil packets on a baking sheet and bake in the oven for 25-30 minutes, or place them on the grill for about the same time. They’re done when the potatoes are tender and the cheese is melted.
Carefully unwrap the packets (watch out for steam!) and serve the cheesy sausage potato foil packets hot.