If you’re using bamboo or wooden skewers, soak them in water for 30 minutes. Meanwhile, start the coals or heat a gas grill for medium-high cooking. Make sure the grates are clean.
Cut the fish and the bread into 1-to 1 1/2-inch cubes. Toss the fish with 2 tablespoons of the oil in one bowl and the bread with the remaining 4 tablespoons oil in another. Season with salt and pepper.
Slice off the peel at the top and bottom of an orange and set it, flat side down, on a cutting board. Cut downward to remove the peel, pith, and membrane to reveal the fruit. Then cut each orange section on both sides to remove it from the membrane. As you work, put the sections in a bowl. Repeat with the remaining oranges. Thread the fish, bread, and orange sections onto skewers, alternating them; save any juice that has accumulated in the bowl.
Put the skewers on the grill directly over the fire. Close the lid and cook until the croutons are golden and the fish is just cooked through (peek inside in a few places to check), 4 to 5 minutes per side. Transfer to a platter, pour over any reserved orange juice, and serve.
Adapted from How to Grill Everything, © 2018 by Mark Bittman. Reproduced by permission of Houghton Mifflin Harcourt.