Rinse and soak the black-eyed peas overnight in water.
Drain and rinse the soaked peas; set aside.
In a large pot, sauté the diced onion in a splash of oil over medium heat until translucent, about 5 minutes.
Add minced garlic and sauté until fragrant, about 1 minute.
Stir in the soaked black-eyed peas, chicken broth, ham hock, thyme, cayenne, salt, and pepper.
Bring the mixture to a boil, then reduce heat to low and cover.
Simmer for about 45 minutes to 1 hour, or until peas are tender.
Taste and adjust seasoning as needed before serving.