Preheat your oven to 375º F.
Peel and dice the onion.
Melt the butter in a saucepan until it starts to sizzle, but before it begins to color. Add the onion and cook on medium-high in the butter for about 5 minutes. Next, add the rice and the bay leaf (make an incision). Stir the rice with the onions and let the rice become transparent (nacre in French) for 2 minutes. Cover with 800g of water, bring to boil and stir again.
Cover the saucepan, and cook the rice in the oven for about 20 minutes at 375 °. Check from time to time. The rice should be cooked when the water has completely evaporated. If the rice isn’t cooked, then add more boiling water.
Salt and pepper to your taste.
TO COOK THE SOLE
Flour the soles and shake off any excess flour.
In a large non-stick pan, heat 25g of the clarified butter until it reaches a gentle sizzling. Take the sole by the head and place it in the butter. Cook the sole in the clarified butter, and lower the flame if it gets too high. When the coloration starts getting golden, place a spatula under the tail and cook for two more minutes. Baste the fish with the clarified butter frequently.
Flip the sole gently by the head. Baste it again with butter and let it cook with the spatula underneath the tail.
Repeat for each sole.
TO MAKE THE BROWN BUTTER
Heat the remaining 100g of butter until it starts caramelizing. Once it has browned, deglaze with the lemon juice. Be careful not to let it burn.
Sprinkle the parsley and the brown butter generously on the sole. Salt and pepper to your taste.
Serve with the pilaf rice.