Preheat oven to 350 degrees Fahrenheit.
Over low heat, melt butter in a pan. Add chopped onions and a pinch of salt, and saute until translucent. Add the garlic and cook for one minute.
Once the garlic and onions have sweat, add the spinach and lemon zest until warmed through. Add salt, pepper and parsley, stirring well to combine everything. Remove heat and cover pan.
Over medium heat, warm the heavy cream and wine in a saucepan. As the liquid simmers, add cheese in small additions, stirring well until melted.
Season both sides of the flounder fillets with salt and pepper. Spread the spinach mixture onto each fillet, and roll tightly.
In a casserole dish, spread cooked rice evenly, Place the flounder, seam-side down, on the rice and pour the creamy cheese sauce over each fillet.
Cook uncovered for about 25 minutes. Once cooked, let cool for 5 minutes before serving.