Mix ground beef, panko, onion soup mix, and black pepper in a bowl.
Shape into four 4-inch patties, 1/2 inch thick.
Press a small indentation into the center of each patty.
Heat 1 tablespoon butter in a 12-inch nonstick skillet over medium-high heat.
Cook patties 4 minutes per side until browned and internal temperature reaches 130°F.
Remove patties to a plate and cover with foil.
Reduce heat to medium and add sliced onions to the skillet.
Cook onions 4 minutes until light brown and softened.
Sprinkle flour over onions and cook 1 minute, stirring constantly.
Gradually whisk in beef broth and bring to a boil.
Simmer 4 minutes until sauce thickens.
Remove from heat and stir in remaining 2 tablespoons butter.
Season with salt and pepper to taste.
Pour gravy over patties, garnish with chives, and serve immediately.