Mix beef, panko, soup mix, and pepper; form four patties with a center indentation.
Melt butter; cook patties 4 min per side until 130°F; tent to keep warm.
Sauté onion 4 min; stir in flour and cook 1 min; whisk in broth and boil until thickened, 4 min.
Stir in remaining butter; season gravy.
Serve patties topped with gravy and chives.