Preheat the oven to 375°F and lightly grease a 12-cup muffin tin.
Heat the olive oil in a skillet over medium heat. Add the mushrooms and onion, then cook for 5 to 7 minutes until the vegetables soften and most liquid evaporates. Stir in the garlic and cook for 1 minute more.
Transfer the mushroom mixture to a large bowl and let it cool for a few minutes. Add the ground turkey, breadcrumbs, egg, Worcestershire sauce, thyme, salt, and pepper. Mix with your hands until just combined.
Divide the mixture into 4 equal portions. Flatten each portion slightly, place one cube of Swiss cheese in the center, and shape the meat around the cheese to fully enclose it. Press each one into a muffin cup.
Bake for 22 to 25 minutes until the internal temperature reaches 165°F. Let the meatloaves rest in the tin for 5 minutes before serving.