1. Adjust oven rack to middle position and heat oven to 450°. Brush rimmed baking sheet with 1 tablespoon oil. Toss potatoes with 1 tablespoon oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper together in bowl. Place potatoes, cut side down, on half of sheet. In now-empty bowl, toss beans with 1 tablespoon oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper, then place on empty side of sheet. Roast until potatoes are light golden brown and beans are well browned, 15 to 20 minutes, rotating sheet halfway through baking.

2. Meanwhile, toss bread crumbs with remaining tablespoon of oil in shallow dish and season with salt and pepper. Microwave crumbs, stirring often, until deep golden brown, 3 to 5 minutes. Let crumbs cool slightly, then stir in dill. In separate bowl, mix mayonnaise and mustard together. Season fish with salt and pepper, brush top of fish with mayonnaise mixture, and press bread crumbs into mayonnaise to adhere.

3. Remove sheet from oven and reduce oven temperature to 275°. Transfer beans to platter and cover with foil. Lay fish, breaded side up, on now-empty side of sheet and continue to roast until center of fish is still translucent when checked with tip of paring knife and registers 140 degrees, about 15 minutes. Transfer potatoes and fish to platter with beans and serve.