1. In a 12- by 17-inch rimmed pan, mix potatoes, onion, rosemary, 3 tablespoons olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Spread into a single layer. Bake on upper rack in a 425° regular or convection oven for 10 minutes.
2. Meanwhile, oil a 10- by 15-inch rimmed pan. In a bowl, mix 2 tablespoons soy sauce and 2 teaspoons oil. Put sesame seeds on a plate. Roll drumsticks in soy mixture (add more soy if needed), then in sesame seeds to coat. Lay drumsticks well apart in pan. When potato mixture has baked 10 minutes, place chicken on lower rack in oven and bake until well browned (180° in center of thickest part), 30 to 35 minutes.
3. When potatoes begin to brown at pan edges, about 10 minutes after adding chicken, turn with a spatula, moving unbrowned ones to edges; spread level. Bake until potatoes are tender when pierced, 15 to 18 minutes longer.
4. While potatoes cook, put croutons into a heavy zip-lock plastic bag and coarsely crush; mix with remaining 2 tablespoons olive oil. When potatoes are done, mix in crushed croutons and bake until browned, 5 to 8 minutes.
5. Arrange chicken on a platter with hash. Add more salt and pepper to taste.