Bring 1 cup water to a boil in a small pot. Add couscous, 1/4 teaspoon salt, and 1 teaspoon ginger. Remove from heat, cover, and let stand 5 minutes. Add 1/2 teaspoon zest; fluff with a fork.

Melt butter in a large straight-sided skillet over medium-high heat. Add white and light-green parts of scallions; cook 30 seconds. Add carrots, miso, and remaining 1 1/2 teaspoons ginger. Whisk in 1 cup water; bring to a boil, then cover, reduce heat to low, and simmer 3 minutes.

Season fish with salt, pepper, and remaining 1 teaspoon zest. Add to skillet with asparagus, cover, and cook 5 to 6 minutes. Serve over couscous, sprinkled with scallion tops, with lemon wedges alongside.