Chef John's Salisbury Steak

Ingredients

• 1 pound ground beef (85% lean)
• ½ cup bread crumbs (plain)
• 1 large egg (beaten)
• 2 tablespoons ketchup
• 1 tablespoon Worcestershire sauce
• 1 teaspoon dry mustard
• 1 teaspoon soy sauce
• ½ teaspoon freshly ground black pepper
• 1 pinch cayenne pepper (or to taste)
• 2 tablespoons salted butter
• 12 large white button mushrooms (sliced)
• 1 cup diced onion
• Salt (to taste)
• 2 tablespoons all-purpose flour
• 3 cups high-quality, low-sodium beef broth