Preheat oven to 450 degrees.
Arrange each piece of fish in the center of the parchment paper and sprinkle with a pinch of sea salt and pepper.
Toss the fennel and shallot in a bowl with a light drizzle of olive oil and season with a pinch of salt and pepper.
Top each filet with a fourth of the fennel, shallot and olives. Add a thyme sprig to each filet and 2 slices of lemon. Drizzle with 1 tablespoon of wine over each filet and top with 1 teaspoon of butter for each.
Bring 2 opposite sides of the parchment together and fold. Continue to fold all the way down until you reach the fish. Twist both ends of the parchment so that it looks like a hard candy wrapper. Repeat for each piece of fish. Place each packet on a baking sheet and bake for 10-12 minutes based on the thickness of the fish.
Transfer each packet to a plate and use caution when opening – the steam will be very hot!