Position the racks in the top third of and center of the oven and preheat to 400*F. Cut six 9 x12 inch pieces of baking parchment paper. Mix the salt and pepper together.
Place a piece of parchment on the work surface with one short end facing you. Fold the paper crosswise in half to make a crease, and unfold. Place two pieces of butter on the bottom half of the paper. Place a snapper fillet on the butter and season lightly with the salt and pepper. Sprinkle with 2 teaspoons of the shallots. Top with about 3 tablespoons sugar snap peas, 3 baby carrots, 1 lemon slice and 2 sprigs of thyme. Sprinkle with 1 tablespoon of the wine. Fold the paper over to enclose the fish and vegetables, and tightly fold the open sides closed. Repeat with the remaining parchment paper and ingredients. Place the packets on 2 large baking sheets. (The packets can be prepared up to 4 hours ahead and refrigerated.)
Bake, switching the position of the sheets from top to bottom halfway through baking for even cooking, until the paper is well browned, 15 to 20 minutes. Transfer each packet to a dinner plate and serve, allowing each guest to cut open the packet at the table.
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