Make the patty mixture. In a large bowl, combine ground beef, breadcrumbs, egg, milk, grated onion, garlic, Worcestershire, Dijon, onion powder, paprika, salt, and pepper. Mix gently with your hands or a fork until just combined. Avoid overmixing.
Shape the patties. Divide into 4 oval patties, about 3/4-inch thick.
Use your thumb to press a shallow dimple in the center of each to help them cook evenly.
Preheat the air fryer. Set to 375°F (190°C) for 3–5 minutes. Lightly spray the basket with oil to prevent sticking.
Air fry the patties. Arrange patties in a single layer with space between them. Cook for 9–12 minutes, flipping halfway.
Internal temperature should reach 160°F (71°C).
Start the gravy. While the patties cook, heat butter and olive oil in a skillet over medium heat. Add onions and a pinch of salt; cook 4–5 minutes until softened. Add mushrooms and cook another 5–6 minutes until browned and reduced.
Thicken the gravy. Sprinkle flour over the onion-mushroom mix.
Stir for 1 minute to cook off raw flour taste. Slowly whisk in beef broth, then add Worcestershire, Dijon, and thyme. Simmer 3–5 minutes until slightly thickened.
Season with salt and pepper.
Combine and serve. Nestle cooked patties into the gravy or spoon gravy generously over them. Finish with chopped parsley. Serve hot with your favorite side.