Prep the produce: Wipe the mushrooms clean.
Finely chop half of them and thinly slice the rest. Slice the onion and mince the garlic.
Sauté the mushroom-onion topping: In a large skillet over medium heat, warm 1 tablespoon oil. Add sliced mushrooms and onions with a pinch of salt.
Cook 8–10 minutes, stirring occasionally, until browned and soft. Add half the garlic for the last minute. Set aside and keep warm.
Make the patty mix: In a bowl, gently combine ground beef, finely chopped mushrooms, Worcestershire, Dijon, remaining garlic, a few grinds of pepper, and 1/2 teaspoon salt.
Mix with a fork or your hands just until combined. Do not overwork.
Form the patties: Divide into 4–6 equal patties, about 1/2–3/4 inch thick. Press a small dimple in the center of each patty to prevent doming.
Optional yogurt spread: Stir Greek yogurt with lemon juice, a pinch of salt, black pepper, and a little Dijon.
Chill until serving.
Cook the patties: Heat a grill or skillet over medium-high. Brush with oil. Cook patties 3–4 minutes per side for medium, or to your preferred doneness.
In the last minute, top each with Swiss and cover to melt.
Toast the buns: Lightly oil the cut sides and toast on the grill or in the skillet until golden.
Assemble: Spread yogurt or Dijon on buns. Add greens, the cheesy patty, and a generous spoon of the mushroom-onion mixture. Finish with tomato if you like.
Rest and serve: Let the burger sit 2 minutes to settle the juices, then serve hot.