Cover arame with water; let stand 15 minutes. Drain.
Brush tofu slices with 1 teaspoon oil. Heat a large nonstick skillet over medium-high heat. Add tofu, and cook until liquid from tofu is evaporated (3 minutes). Remove tofu from pan. Cool and cut into 1/4-inch pieces, and set aside.
Heat 2 teaspoons oil in pan over medium-high heat. Add carrot, onions, and ginger; cook 4 minutes or until carrot is golden brown, stirring frequently. Stir in arame and salt; cook 3 minutes or until arame is tender. Stir in tofu and soy sauce. Cook for 5 minutes or until thoroughly heated. Serve with rice. Sprinkle with sesame seeds.
Note: Seaweed is sold at health-food stores and Asian supermarkets.