In a large shallow bowl whisk together milk, eggs, 1 tablespoon rum and 2 teaspoons sugar. Soak bread triangles 30 seconds per side, until well-coated. In a large cast-iron or nonstick skillet melt 2 tablespoons of the butter over medium-low heat. When butter bubbles, carefully transfer brioche triangles to pan and cook 1 to 1 1/2 minutes per side, or until golden brown. Arrange triangles and ice cream decoratively on 4 dessert plates, standing toasts on their edges.
In another skillet, melt remaining 4 tablespoons butter over medium heat. In a small bowl, toss banana slices with lemon juice and remaining 3 tablespoons sugar. When butter bubbles, add bananas and cook, turning them once, until each side is glazed light brown, about 3 minutes per side. In a small pan warm remaining 1/2 cup rum and pour over bananas. Heat one minute, then carefully light with a long match. Shake pan until flames subside and pour over toasts and ice cream. Sprinkle with confectioners' sugar and serve immediately.