Heat 1 tablespoon oil in a medium skillet over medium heat. Add onion and sugar; cook, stirring occasionally, until onions are golden, 6 to 8 minutes. Reduce heat to low; cover, and cook, stirring occasionally, until onions are caramelized, about 10 minutes. Set aside.
Slice each apple lengthwise into 4 rounds (about 1/4 inch thick). Heat remaining tablespoon oil in a large nonstick skillet over medium heat. Lay apple slices in single layer; cook until they begin to soften and slightly color, about 3 minutes per side. Remove from heat.
Preheat oven to 300 degrees. Using a 2-inch round cookie cutter, cut out one round from each bread slice. Arrange rounds on baking sheets; place in oven to dry out and toast slightly, 5 to 7 minutes per side. Transfer to a wire rack to cool.
Using a small offset spatula, spread butter on each round; cover with an apple slice. Using a pastry bag fitted with an Ateco #863 star tip, pipe 1 teaspoon brandade onto each, and top with caramelized onion. Serve immediately.