Begin by preheating your oven to 400°F (200°C). Tear off a large piece of aluminum foil and lay it on a baking sheet, then lightly brush the center with oil. Place the whole sea bass on the prepared foil and tuck 3 sprigs of tarragon along with all but 1–2 slices of lemon into the fish’s cavity. Season the inside generously with salt and black pepper.
Season the outer surface of the fish as well, then carefully lift up the sides of the foil to create walls around the fish. Drizzle the wine over the top of the sea bass, allowing it to pool around the fish. Bring the edges of the foil together and seal them to form a loose but secure package, leaving a little room inside for steam to circulate. Transfer to the oven and bake for approximately 30 minutes, or until the fish flesh turns opaque and flakes easily when gently tested.
While the fish is baking, prepare the lemon butter sauce: in a saucepan, whisk together the half-and-half, lemon juice, butter, egg yolk, and flour until everything is well combined and smooth. Place the pan over very gentle heat and stir constantly, being careful not to let it boil, until the mixture thickens enough to coat the back of a wooden spoon. Season with salt and white pepper to taste, then fold in the chopped tarragon. Keep the sauce warm over the lowest heat, stirring occasionally.
When the fish is cooked through, carefully unwrap it from the foil and transfer the sea bass to a warmed serving platter. Pour any accumulated cooking juices from the foil packet over the fish for extra flavor and moisture. Arrange the reserved lemon slices and remaining tarragon sprig on top as an attractive garnish, and bring to the table immediately while still hot. Serve the warm lemon butter sauce on the side in a separate pitcher or bowl for guests to help themselves.
