Preheat the oven to 350°F and lightly grease a loaf pan.
In a skillet over medium heat, cook the chopped mushrooms and diced onion until softened and most of the liquid has evaporated, about 6 minutes. Stir in the minced garlic and cook for 1 minute more. Remove from heat and let cool slightly.
In a large bowl, combine the ground beef, crushed saltine crackers, shredded Swiss cheese, fresh thyme, egg, milk, salt, and pepper. Add the cooled mushroom mixture.
Mix everything together with your hands until evenly combined, but avoid overworking the meat.
Transfer the mixture to the prepared loaf pan and press it down evenly.
Bake for 50 to 55 minutes, or until the internal temperature reaches 160°F. Let the meatloaf rest for 10 minutes before slicing.