In a large stockpot or Dutch oven, combine peas, 1 teaspoon salt and enough water to cover. Simmer peas over medium low heat until tender, about 20 minutes.
Drain peas and set aside.

Heat Dutch oven over medium heat and add the oil and onion. Cook and stir the onion until tender about 5 minutes. Add the garlic and continue to cook another minute. Add the tomatoes, thyme, vinegar, sugar and red pepper flakes.
Cook another 15 minutes, stirring occasionally. Add the black-eyed peas and continue to cook for 15 more minutes.

Stir in the cooked rice and parsley.
Season with salt and freshly ground pepper to taste.

Serve while hot.