Heat the olive oil in a medium pan over medium heat.
Add the celery, leeks, carrots, and a pinch of salt and white pepper, and sauté until the vegetables start to cook down.
Add the cream and stir to coat the vegetables. Cook until the cream is thickened.
Remove the pan from the heat.
Line a baking sheet with parchment paper. Roll out both sheets of puff pastry until they are ⅓-inch thick. Transfer one sheet of puff pastry to the baking sheet.
Cut the sea bass along the back to remove the spine, then butterfly open. Season with salt, pepper, and the tarragon.
Scoop the cooked vegetables onto one side of the fish, then fold over the other fillet.
Transfer the fish to the center of the sheet of puff pastry.
Brush egg wash around the fish, then lay on the second sheet of puff pastry, pressing around the fish to seal. Use a paring knife to cut away the excess puff pastry in the shape of a fish.
Brush the top of the puff pastry with egg wash and use the leftover pastry scraps to decorate the fish with an eye and gills. Use the tip of the knife or the large opening of a pastry tip to draw scales on the body and tail.
Chill in the refrigerator for at least 30 minutes.
Make the Chive Butter Sauce: In a medium saucepan over medium heat, combine the wine, lemon juice, shallots, and tarragon. Reduce until only a ¼ cup (60 ml) of liquid remains. Add the cream and reduce until the mixture thickens slightly.
Slowly whisk in the butter, 1 piece at a time, until the sauce is glossy and thickened.
Remove the tarragon stem and season with salt and pepper. Stir in the chives.
Preheat the oven to 375℉ (190℃). When the oven is heated. Bake the fish for 15 to 20 minutes, or until the pastry is golden brown.
Transfer the fish to a platter and garnish with fresh parsley and lemon wedges.
To serve, cut the fish into individual portions and plate with a drizzle of Chive Butter Sauce.