6large squares of parchment paper or aluminum foil
Preheat oven to 400°F.
Place 4 asparagus spears in the center of each parchment or foil square. Place a fillet on top of the asparagus. Coat each fillet with 1 teaspoon of olive oil. Season with salt and pepper.
Spread 2 teaspoons of pesto on each fillet. Top fillets with about a ¼ cup of fennel slices, 3-4 sprigs of thyme, and 1 teaspoon dill.
Divide the lemon zest evenly among the fillets. Next, top each with 1 lemon slice and 2 teaspoons vermouth. Season again with salt and pepper.
Fold up parchment or foil and seal edges to enclose completely. Transfer packets to a large, rimmed baking sheet. (Packets can be made 4 hours ahead. Chill. Remove from refrigerator 30-45 minutes before baking.)
Bake packets in preheated oven for 15 minutes. Let them rest 5 minutes before serving.
Transfer packets to plates. Be careful opening due to hot steam. Garnish with fennel fronds, and serve with crusty bread to mop up juices, if desired.