Make the bread pudding: Bring 4 cups milk, 16 tbsp. butter, sugar, vanilla, nutmeg, and salt to a simmer in a 4-qt. saucepan over medium-high heat; remove from heat, and let cool for 20 minutes. Combine bread, chocolate, and almonds in a large bowl; set aside. Add 6 eggs to milk mixture, and whisk until smooth. Pour custard over bread mixture, and stir until evenly combined; let sit to soften bread, about 20 minutes. Heat oven to 300°. Pour bread mixture into a 9" × 13" metal baking pan, making sure ingredients are evenly distributed, cover with foil, and bake until set, about 1 hour. Let cool to room temperature, and then refrigerate until chilled, at least 2 hours or overnight.
Meanwhile, make rum sauce: Bring sugar and ½ cup water to a boil in a 2-qt. saucepan over high heat, stirring until sugar dissolves; cook, without stirring, until sugar turns into an amber-colored caramel, about 15 minutes. Add cream, butter, rum, and juice, and stir until smooth; set sauce aside.
Place flour and bread crumbs in separate shallow dishes; whisk together remaining milk and eggs in a third shallow dish. Unmold bread pudding from pan, and cut into 8 rectangles. Heat 2 tbsp. butter in a 12" skillet over medium heat. Dredge each piece in flour, then coat in the milk mixture, and finally coat in bread crumbs. Add 4 pieces to skillet, and cook, turning once, until golden brown on both sides, about 6 minutes. Transfer to paper towels to drain briefly; repeat with remaining butter and pieces. While pudding is still hot, top each with a chunk of white chocolate.
To serve, place turbinado sugar on a plate, and dip the flat cut-side of each banana quarter in sugar to cover completely; place sugar-side up on a foil-lined baking sheet. Using a handheld blowtorch or the broiler, heat sugar until melted and caramelized, about 6 minutes if broiling; set aside. Pour rum sauce in the middle of 8 serving plates, and place 1 piece pudding in the center of each; place 2 bruleed banana quarters on either side of the bread pudding.