Prepare the parchment: Preheat your oven to 400°F. Cut four sheets of parchment paper, each measuring about 18 inches long.
Season the fish: Lay one fish fillet in the center of each parchment sheet. Sprinkle a small amount of salt and freshly ground black pepper on the fillets. Drizzle a little olive oil over the fish.
Layer the toppings: Place three thin slices of lemon over each fish fillet, slightly overlapping them so they cover the top. Distribute one-quarter of the corn kernels, asparagus slices, and cherry tomatoes (if using) evenly around each fillet.
Add final seasoning: Drizzle another small amount of olive oil over the vegetables and fish, then lightly season everything with a pinch of salt and pepper again.
Seal the packets: Bring the long edges of the parchment paper together over the fish and vegetables. Fold the edges downward several times to form a tight seal, leaving a little space inside for steam. Twist the open ends of the parchment in opposite directions to secure them tightly.
Repeat and bake: Repeat this process for all four packets, placing them on a baking sheet as you go. If you’re not baking them immediately, refrigerate the packets for up to 4 hours. Otherwise, bake the packets in the preheated oven for about 15 minutes, or until the parchment puffs up and the fish is cooked through.
Serve: After removing the packets from the oven, let them rest for about 5 minutes. Use scissors to cut an X in the top of each packet, and gently pull the parchment back to reveal the fish and vegetables. Sprinkle the finished dish with freshly chopped herbs and serve right away.