1. Bake mangoes: Preheat oven to 400 degrees. Slice mangoes into 4 pieces; cut each piece into 1/2-inch-thick slices. Pour butter into a 9-by-13-inch glass or ceramic baking dish. Add mango slices and sprinkle with brown sugar; toss to coat. Arrange slices in one layer. Bake, tossing once halfway through, until mangoes are tender and juice is bubbling, 45 to 50 minutes. While mangoes are baking, prepare tortillas.

2. Prepare tortillas: Stack tortillas and cut in half. In a large bowl, toss tortilla halves with melted butter until well coated. In a small bowl, combine sugar, cinnamon, and 1/4 teaspoon salt. Place tortillas on a large (or two small) rimmed baking sheet; sprinkle both sides with cinnamon-sugar mixture, and arrange in a single layer. Place in oven while mangoes are still baking, and bake until golden and crisp, 10 to 15 minutes. Let cool.

3. Assemble: Divide mango slices among plates. Top with a scoop of vanilla ice cream, if desired, and serve with cinnamon-sugar tortilla halves, broken again in half.