In a large pot of boiling salted water, cook the collard greens over medium-high heat until tender, about 20 minutes. Drain well and set aside.
In a large pot, heat the oil over medium heat. Add the onion, celery, and carrot and garlic. Cover and cook, stirring occasionally, until slightly softened, about 5 minutes.
Stir in the stock, rice, thyme, pepper and salt to taste and bring to a boil. Reduce heat to low and simmer for 15 minutes.
Stir in the potato and black-eyed peas and continue to cook until the vegetables and rice are tender, about 30 minutes. Stir in the cooked collard greens and taste before adjusting seasonings, if necessary. Simmer to heat through and allow the flavors to mingle, about 10 minutes. Serve hot with a bottle of Tabasco at the table.
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