Set grill to medium-high or oven to 400°F (200°C).
Mix beef with Worcestershire, garlic powder, salt, and pepper. Form into 4 patties.
Toss halved potatoes with olive oil, Italian seasoning, salt, and pepper.
Brush 4 foil sheets with oil. Add potatoes, a patty, mushrooms, and onions to each.
Seal packets and grill or bake for 25–30 minutes, until potatoes are tender and patties reach 160°F.
Open packets, top each burger with Swiss cheese, loosely reseal, and rest 2 minutes to melt. Add butter if desired.
Enjoy hot, straight from the foil or on plates.