Preheat the oven to 375 degrees and lightly grease a 12-cup muffin tin.
Heat a skillet over medium heat and cook the mushrooms and onion for 5 to 6 minutes until the liquid evaporates and the vegetables soften. Let the mixture cool for a few minutes.
In a large bowl, combine the ground beef, cooled mushroom mixture, 1/2 cup of the Swiss cheese, breadcrumbs, egg, Worcestershire sauce, garlic, thyme, salt, and pepper. Mix gently with your hands until just combined.
Divide the mixture evenly among the muffin cups, pressing it down lightly to fill each one.
Bake for 20 minutes, then remove the tin from the oven and sprinkle the remaining 1/2 cup of Swiss cheese over the tops.
Return to the oven and bake 5 more minutes until the cheese melts and the internal temperature reaches 160 degrees. Let the muffins rest for 5 minutes before serving.