Place a 12-inch saute pan on the stove, add the shallots, garlic and court bouillon to the pan. Set over a high heat and bring to a boil. Reduce the heat to a gentle simmer and cook for 5 minutes. Season the sea bass fillets on both sides with the salt and white pepper. Place the fillets in the poaching liquid and cover with a lid, or a buttered round of parchment paper. Cook the fish for 5 to 6 minutes, or until cooked through.
Remove the fillets from the poaching liquid using a slotted metal spatula and place on a warm plate loosely covered with aluminum foil. Put the plate in a warm place while you make the sauce. Raise the heat to high and reduce the court bouillon for about 10 minutes, or until reduced to 1/2 cup. Lower the heat, and add the butter to the pan a little at a time. Use a whisk to stir the cold butter into the sauce and season with salt and white pepper. Sprinkle the tarragon and chervil into the sauce and return the fish to the pan. Place the pan over a medium-low heat and warm the fish through, about 1 minute.
In a 10-inch saute pan, set over a medium-heat, add the olive oil and 1 teaspoon of butter to the pan. Once the butter has melted, add the carrots to the pan and saute, stirring often for 1 1/2 minutes. Add the zucchini and 2 tablespoons of water to the pan and continue to cook for 2 minutes more. Season the vegetables with salt and white pepper and divide among 4 warmed entree plates. Place a sea bass fillet over the vegetables and divide the sauce among the 4 plates as well. Garnish with chervil.
Combine all the ingredients into a 4-quart saucepan and bring to a boil. Reduce the heat to a simmer and continue to cook for 45 minutes. Strain the bouillon and use immediately, or cool and refrigerate for later use. The bouillon may also be frozen and kept for several months.