In a small saucepan, bring the champagne to a boil over medium high heat. Reduce heat to simmer until volume is halved.
Whisk in the cream slowly and bring up to a simmer; allow to cook for 5-7 minutes. Add the butter, one cube at a time, whisking constantly, until all the butter has been incorporated. Set aside to let it cool and thicken.
Prepare the marinade/vegetable dressing:
Combine the juice of the lemon with the vinegar and slowly whisk in the olive oil. Add the parsley and salt and pepper to taste.
Roast the vegetables:
Toss the parsnips and potatoes in 1/4 of the dressing. Place on a baking sheet; season with salt and pepper. Roast at 450° for 10 minutes. Stir. Toss the garlic and pearl onions in another 1/4 of the dressing. Add to the potatoes and parsnips and roast for another 10 minutes. Stir. Toss the Brussels sprouts in another 1/4 of the dressing. Add to the rest of the vegetables and roast for 20 minutes, stirring twice. Set aside.
Prepare to broil the fish:
While the vegetables are roasting, brush the turbot fillets with half of the remaining dressing. Allow to marinate for no more than 60 minutes.
Broil the fish:
Once the vegetables have finished, turn the oven to high broil. Brush the turbot with the rest of the dressing and season the tops with salt and pepper. Place in a skillet or a baking sheet that has been lined with tin foil. Broil 3-4 inches from the broiler for 3-6 minutes, depending on thickness, or until the tops of the fillets are golden brown and bubbling. Check on it often - its easy to burn them with this method. Remove from the oven.
Put half of the vegetables on each of two plates that have been warmed briefly in the oven. Drizzle with beurre blanc. Place the fillet on top of the vegetables and drizzle again with beurre blanc. Serve immediately.