Combine first 4 ingredients in a small saucepan. Bring to a boil; reduce heat, and simmer 5 minutes or until onion is tender. Add water; bring to a boil. Gradually add grits, stirring with a whisk until blended. Cover, reduce heat, and simmer 10 minutes or until done.
Heat the oil in a small nonstick skillet over medium-high heat. Add the mushrooms, and sauté for 5 minutes or until golden. Stir mushrooms and cheese into grits. Set aside.
Sprinkle fillets with salt, thyme, and pepper; place the fillets, skin sides down, on a broiler pan coated with cooking spray. Broil for 10 minutes or until fish flakes easily when tested with a fork. Remove skin from fillets; discard skin. Spoon 1/2 cup grits on each of 4 plates; top each serving with a fillet. Sprinkle with parsley.