In a large skillet, heat 3 tablespoons EVOO, 3 turns of the pan, over medium to medium-high heat. Add the onion, season with salt and pepper and cook, stirring occasionally, until browned, 15 to 20 minutes. Stir in the thyme and mustard, then scrape into a bowl and set aside. Wipe out the skillet; set aside.
Pat the cod dry and season with pepper. Wrap each piece of fish in a slice of prosciutto. In a large nonstick skillet, heat half the remaining EVOO over medium-high heat until rippling. Add half the fish fillets and cook, turning once, until the prosciutto is crisp and the fish is firm, 3 to 4 minutes on each side. Cover with foil to keep warm. Repeat with the remaining oil and fish.
Pour water, 1 inch deep, into the onion skillet and bring to a boil. Add salt and the asparagus and cook for 3 minutes; drain. Toss with the reserved onion mixture to coat. Divide among 4 plates and top with the tomato.
Serve the cod and lemon wedges alongside the salad.