Arrange pineapple slices on a non-stick baking sheet; reserve juice.
Combine liver, crumbs, milk, salt and thyme; mix well.
Shape into patties the size of the pineapple rings; top pineapple with patties.
Bake at 400Â° F. until patties are brown on top; turn them gently with spatula and brown second side. (If you prefer, the patties and pineapple rings may be put under the broiler to brown; be sure to turn each patty to brown the second side).
Meanwhile, heat reserved pineapple juice in saucepan, add rice and toss well to heat and separate the grains.
Divide rice evenly into 4 luncheon plates and sprinkle with parsley.