Mix crab, mayonnaise, bell pepper, and parsley and season with salt and pepper.
Lay sole fillets flat with darker side up and season with salt and pepper. Put a good amount of crab mixture onto each fillet, leaving about an inch of fillet on each end.
Starting at one side, roll the fillet up with the crab mixture inside. The finished product should look like a cinnamon roll. Place each roll into an empty space in a greased muffin tin, upright. Bake in oven until just cooked through, about 20 minutes.
Make bread crumbs while sole is baking:
Cook garlic in oil in a small skillet over moderate heat, stirring, until fragrant, about 30 seconds. Stir in bread crumbs and cook, stirring, until golden brown, 4 to 5 minutes. Remove from heat, then stir in zest and season with salt and pepper.
Transfer sole to plates and pour pan juices through a fine sieve into a small bowl. Spoon some of juices over fish and sprinkle with bread crumbs.