How to Make It
In a large, enameled cast-iron casserole, heat 2 tablespoons of the olive oil. Add the onion, carrot and minced garlic and cook over moderate heat, stirring occasionally, until softened, about 6 minutes. Add the drained black-eyed peas, ham hocks, chicken stock and bay leaves and bring to a boil. Reduce the heat to very low, cover partially and cook until the beans are tender, about 1 1/2 hours. Season generously with salt and pepper and let stand for 30 minutes.
Meanwhile, preheat the oven to 350°. Toast the bread slices in the oven for about 8 minutes, until golden. Brush lightly with olive oil and rub lightly with the garlic clove.
Drain the black-eyed peas; discard the ham hocks and bay leaves. Transfer the peas to a serving bowl. Stir in the remaining 1/4 cup of olive oil and season with salt and pepper. Serve the black-eyed peas with the garlic toasts, passing grated cheese at the table.