Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.
Combine the wild rice stuffing mix and chicken broth in a bowl. Let it stand for 5 minutes, or until the stuffing has softened and absorbed most of the broth.
While the stuffing rests, heat the olive oil in a skillet over medium heat. Add the mushrooms and cook for 5 to 7 minutes, stirring occasionally, until softened and their released moisture has evaporated. Let them cool briefly.
In a large bowl, mix the ground beef, egg, Worcestershire sauce, thyme, salt, and pepper. Fold in the cooked mushrooms, chopped green beans, and prepared stuffing until just combined. Avoid packing the mixture tightly.
Divide the mixture among the 8 prepared muffin cups, pressing it in gently. Bake for 20 minutes, until the meatloaf muffins are nearly cooked through.
Place half a slice of Swiss cheese on each muffin. Bake for another 3 to 5 minutes, until the cheese melts and the beef reaches 160°F in the center.
Let the muffins rest in the pan for 5 minutes before serving so they hold together more easily.