Cook the mushrooms. Heat butter and olive oil in a large skillet over medium-high heat. Add mushrooms in an even layer and let them sear without stirring for 2–3 minutes. Stir, then cook until browned and reduced, about 6–8 minutes total.

Add aromatics. Stir in shallot, garlic, and thyme. Cook 1–2 minutes until fragrant. Add Worcestershire, season with salt and pepper, and cook another minute. Transfer to a bowl and cover to keep warm.

Make the turkey mixture. In a large bowl, gently combine ground turkey, grated onion, mayo, Dijon, Worcestershire, salt, pepper, and garlic powder. Mix with a fork or your hands just until combined. Do not overwork.

Form patties. Divide into 4 equal portions and shape into patties about 1/2 inch thick. Press a small dimple in the center of each to prevent doming.

Preheat your cooking surface. Heat a cast-iron skillet or grill to medium-high. Lightly oil the surface.

Cook the burgers. Place patties on the hot surface. Cook 4–5 minutes until browned, then flip. Cook another 3–4 minutes, until the internal temperature reaches 165°F (74°C).

Add the cheese. During the last minute, top each patty with Swiss cheese. Cover the pan or close the grill lid to help it melt.

Toast the buns. In a separate skillet or on the grill, melt butter and toast the buns cut-side down until golden at the edges.

Assemble. Spread Dijon or mayo on the buns. Add lettuce to the bottom bun, then the cheesy turkey patty. Spoon a generous pile of mushrooms on top. Add tomato or pickles if you like, then the top bun.

Serve hot. These are best right away while the cheese is melty and the buns are crisp.