Into a large pot, add the black-eyed peas and cover with 1 inch of cold water. Place the pot on the stove over medium-high heat. Bring to a boil; let the peas boil for 3 minutes. Remove the pot from the heat, cover, and let the peas soak for 1 hour. Drain and set aside. The peas will have softened but still have some "bite" to them. (Skip this step if using canned or fresh black-eyed peas).
Return the empty pot to the stovetop over medium-high heat. Add the olive oil. When the oil is hot, add the liquid smoke, onion, carrots, and celery. Cook, stirring frequently for 3 minutes, just until vegetables are slightly tender.
Add the garlic and cook for an additional 30 seconds. Stir in the collard greens and cook for 3 minutes, just until wilted.
Add the rice, black-eyed peas, and vegan chicken broth. Bring to a boil, then reduce the heat to low. Cover and simmer for 1 hour, or until the peas are cooked to your desired consistency.
Season to taste with black pepper, add a dash of cayenne pepper sauce, if using, and serve hot.