Wash your hands well with soap and warm water for at least 20 seconds.
Wash and cut celery and bell pepper into small pieces.
Peel and cut onion into small pieces.
Peel and mince garlic.
Cut ham into small pieces.
In a colander, rinse and drain black-eyed peas.
Heat oil in a large pot over medium heat. Add celery, bell pepper, onion, garlic, and thyme. Cook, stirring occasionally, until vegetables are softened, 5-7 minutes.
Add broth to pot. Bring to a boil. Add rice. Reduce heat to simmer. Cover and cook for 10 minutes. *The amount of broth needed will vary depending on the type of instant rice you use. Check your package to find out how much you need.
Stir in ham, black-eyed peas, cayenne, salt, and pepper. Simmer, uncovered, for 5 minutes. Remove from heat. Cover and let stand 5 minutes before serving. Serve with hot sauce, if desired.