Divide court bouillon between two 10-inch sauté pans. Place 3 halibut fillets in each. Bring to a simmer and cook for approximately 3 minutes on one side; turn over and cook for 3 more minutes.
Divide hot eggplant pancakes among 6 plates. Place halibut on top. With 2 tablespoons, make 6 quenelles from the tomato confit to place on top of each plate. Drizzle each with 1/2 ounce each of olive oil and 25-year-old balsamic vinegar.