Remove skin from trout and flake fish, removing any bones. You should have about 2/3 cup.
Heat oil in a large cast-iron skillet over medium-high heat. Add scallions and saute until they start to brown, 2 to 3 minutes. Add potatoes and cook, stirring, until they brown in spots and become crusty, 7 to 8 minutes more.
Stir in milk and cook, scraping up any browned bits, 1 to 2 minutes. Stir in trout and 2 tablespoons dill and cook until heated through. Season with salt and pepper. Serve immediately, topped with sour cream and remaining 1 tablespoon dill.
Ingredient note: Smoked trout can be mail-ordered from Ducktrap River Fish Farm, ducktrap.com. Or use smoked salmon or lox.
4 starch, 1/2 vegetable, 1 1/2 lean meat, 1 fat