Soak black-eyed peas: Place peas in a large bowl; cover with cool water to 3 inches above peas. Let stand at room temperature at least 4 hours or up to overnight. Drain.
Cook aromatics until soft, then add remaining ingredients to Dutch oven: Heat oil in a Dutch oven over medium. Add garlic, celery, and onion to pan; cook until softened, 8 to 10 minutes, stirring occasionally. Stir in chicken stock, bay leaves, thyme sprigs, ham hocks, and drained peas; bring to a boil over high heat.
Simmer peas: Reduce heat to low or level required to maintain a simmer; cover and simmer for 1 hour.
Remove ham hocks: Uncover pan and remove ham hocks to a plate. Stir salt and pepper into peas; simmer, uncovered, until peas are tender, about 45 minutes.
Shred meat from hocks: Meanwhile, when ham hocks are cool enough to handle, pick meat from hocks and finely shred (there won’t be much); discard bones, skin, and gristle. Stir meat into peas. Discard bay leaves and thyme sprigs before serving.
