In a large pot or Dutch oven, heat extra virgin olive oil over medium heat or omit and use vegetable broth in step 2 to prevent onion and garlic from sticking to pot.
Add onions. Sauté briefly until translucent and fragrant. Add bell peppers and carrots. Cook for 5 minutes, tossing regularly. Add garlic and cook for 1-2 minutes more.
Add diced tomatoes (with their juices), water or vegetable broth, bay leaf, spices, salt and pepper. Raise the heat and bring to a boil.
Add in black eyed peas. Boil for 5 minutes, then lower heat. Cover part-way and let simmer for 25 to 30 minutes (occasionally check to stir. If the black eyed pea stew looks too dry, add a tiny bit of water.)
Stir in lemon juice and parsley.
To serve, transfer to bowls. Enjoy with a side of warm Greek pita bread or on top of orzo, rice, or your favorite grain.