Cook rice according to the package directions. Adjust an oven rack to the middle position and heat broiler.
Mix hoisin sauce and 1 tablespoon water in a small bowl. Place fish, skin-side down, on a foil-lined baking pan and spread sauce over the top.
Toss asparagus, mushrooms, oil, and ¼ teaspoon each salt and pepper in a medium bowl. Scatter vegetables evenly around fish.
Broil, stirring vegetables once, until they are tender and fish is cooked through and opaque, 6 to 8 minutes, depending on thickness.
Slide a spatula between the skin and the fish; discard skin. Divide fish among individual plates. Serve with vegetables and rice.