Heat the oven to 400Â°F. Combine the butter and brown sugar in a bowl and microwave until the butter and sugar have melted together, about 30 seconds. Stir in the mustard, honey, and soy sauce.
Toss the asparagus with 1 tablespoon of the oil, the Parmesan, and some salt and pepper. Place the stalks in a baking dish and roast until they're al dente, 10 to 12 minutes.
Meanwhile, heat the remaining tablespoon of oil in an ovenproof skillet over high heat. Season the fillets with salt and pepper and add them to the pan, flesh side down. Cook them until browned on one side, 3 to 4 minutes. Then flip them, brush on half the honey mustard, and place the pan in the oven. Bake until the salmon is firm and flakes easily (but before white solids begin to form on the surface), about 5 minutes. Remove the fillets from the oven and brush them with more honey mustard. Serve the salmon with the asparagus.