Heat olive oil in a large skillet over medium heat. Add onion and cook until slightly softened, about 3-4 minutes. Add garlic and cook another minute, stirring often.
Add chopped mushrooms to pan and cook until they begin to release water. Sprinkle with thyme and salt. Cook, stirring often until most of the liquid has evaporated.
Stir in spinach and cook until completely wilted, about 2-3 minutes. Reduce heat to low. Add brown rice to the skillet and stir to combine. Reduc
Sprinkle grated swiss over the rice mixture, and stir until the cheese is melted. {You should see stringy melted cheese as you stir.} Cool until it is a comfortable temperature for handling.
Meanwhile, place breadcrumbs into a bowl or on a small plate. Prepare a small baking pan by lining with parchment paper or foil sprayed with a bit of oil.
Using a ½ cup measuring cup, scoop out a portion of the rice mixture and shape into a ball, then gently flatten into a patty.
Carefully place patty in the breadcrumbs and press down a bit to adhere, then flip and repeat.* Place onto prepared baking pan. Cover and refrigerate for at least an hour.