In a large pot or Dutch oven, heat extra virgin olive oil over medium heat till shimmering but not smoking. Add onions and garlic. Saute briefly until translucent and fragrant. Add bell peppers and carrots. Cook for 5 minutes, tossing regularly.
Now add diced tomatoes (with their juices), vegetable broth, bay leaf, spices, other optional vegetables, salt and pepper. Raise the heat and bring to a boil. Add in the 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.)
Finally, stir in lemon juice and parsley.
To serve, transfer to bowls. Add a generous drizzle of extra virgin olive oil. Enjoy with a side of warm Greek pita or on top of orzo, rice, or your favorite grain.