Cooking the fish in parchment packets makes sure it doesn't dry out. Bonus: Clean-up is a snap!
Preheat the oven to 400°. Cut out 4 large sheets of parchment paper (about 12 by 16 inches each). In a medium bowl, mix the parsley, oil, shallots, capers, vinegar, garlic, and Dijon; season with salt and pepper. Add the asparagus and toss until coated. Lift the asparagus out of the parsley oil and transfer to a plate. On a work surface, arrange the sheets of parchment so the shorter sides are at the top and bottom. Dividing evenly among the sheets, spoon the remaining parsley oil onto the bottom half of each sheet.
Season the fish. Place 1 fillet on top of the parsley oil on each sheet of parchment. Place 3 asparagus spears on each side of each fillet. Fold the top half of the parchment over the fish, then fold the edges over and crimp to seal each packet. Transfer the packets to a baking sheet.
Bake the parchment packets until a knife inserted through the parchment slides easily into the fish, about 15 minutes. Place 1 packet on each of 4 plates. Carefully open the packets. (There may be steam.) Garnish with the lemon wedges.