Preheat the oven to 375° F.
Place the catfish on a sheet tray, drizzle each side lightly with olive oil, and season with salt and pepper. Bake for 12 minutes, remove from oven and allow to cool slightly before flaking into a large bowl.
In a small skillet over medium-high heat, add butter, oil, prosciutto, garlic, shallots and bay leaves. Cook 4 minutes; remove from heat and let cool slightly before adding to the bowl with the catfish. Add the rice, cheese, parsley and egg. Mix well with a spatula until all ingredients are well incorporated.
Using your hands, form the mixture into balls slightly larger than a golf ball. Make an indentation with your thumb, and place the cheese in the center. Add a bit more of the mixture to fill the hole and reshape.
Place the panko on a plate, and coat the rice ball in panko by rolling over the crumbs. Cook in a deep fryer at 360° F for 3 ½ minutes, or until golden brown.