Heat oven to 400° F. In a medium bowl, mix together the chili and 1 cup of the cheese. Arrange the bell peppers, cut-side up, in a 9-by-13-inch baking dish; season with 1/2 teaspoon salt and ¼ teaspoon black pepper. Divide the chili mixture among the bell peppers, add ½ cup water to the baking dish, and tightly cover the dish with foil.
Bake until the bell peppers are soft, 30 to 40 minutes. Uncover, sprinkle with the remaining cup of cheese, and bake until the cheese is melted, 5 to 7 minutes more.
Meanwhile, in a large bowl, whisk together the lime juice, oil, sugar, ½ teaspoon salt, and ¼ teaspoon black pepper. Add the cabbage and toss to combine. Serve with the bell peppers, sprinkled with the scallions.