Heat the oil in a soup pot. Stir in the onions and cook and stir until they are translucent. Add the garlic and cook and stir another minute or so. Add the vegetable broth, chopped greens, tomatoes and their juice, black-eyed peas, vinegar, brown sugar, thyme, allspice, hot pepper sauce and salt. Simmer for 15 minutes. Stir in the rice and simmer another 5 minutes. Season to taste with more salt and hot pepper sauce, if desired.