Preheat oven to 375F. Spray 12-cup muffin pan with baking spray or line with baking cups.
Heat oil in a wok or large nonstick skillet over medium-high heat. Add garlic, onion, and mushrooms and cook until softened and fragrant, about 3-5 minutes. Add chicken and rice, and cook until warmed through. Add ketchup and soy sauce, and stir until well-combined. Make sure not to over stir to prevent rice from becoming too mushy. Finally, add in cheese (save about ⅓ cup), and stir until melted through.
Divide rice mixture into 12 equal-sized portions (I used a large ice cream scooper), and using your hands, pack tightly and shape into balls. Sprinkle remaining cheese evenly on top and bake for 25-30 minutes, until cheese is melted and bubbly.
Important: Leave the rice balls in the pan to cool completely before taking them out. Otherwise, they will not hold together.