1. Preheat oven to 375 degrees. Soak bread in milk until almost all milk is absorbed. Squeeze out milk; discard. Set bread aside.

2. Heat oil in a large skillet over medium heat until hot but not smoking. Add onion; cook, stirring occasionally, until translucent, 4 to 5 minutes. Reduce heat to low; add two-thirds of crabmeat, the soaked bread, rum, tomato paste, lemon juice, and egg yolk; cook, stirring, 4 minutes. Add cilantro; season with salt, pepper, and hot sauce.

3. Continue to cook mixture, stirring, until combined and crabmeat is broken up, about 5 minutes more. Remove from heat; add remaining crabmeat.

4. Mound the crab mixture into shells; transfer to rimmed baking sheets. Stir breadcrumbs into butter in a small bowl; sprinkle mixture on tops of crab cakes.

5. Bake crab cakes until heated through and brown, 15 to 18 minutes. Serve warm.