Place the black-eyed peas in a large pot and cover with 2 inches of water. Bring to a boil, then drain. Return the black-eyed peas to the pot, add half of the onion and half of the garlic, and cover with 2 inches of water. Set over medium-high heat and bring to a simmer. Add the bay leaf, and reduce heat to medium-low. Cover, and simmer for 30 minutes, until the black-eyed peas are just barely tender. Set a colander over a bowl, and drain, reserving all the cooking liquid.
Preheat oven to 350℉. Place the tomato paste in a small bowl, and add 1/2 cup of water. Whisk to combine. Set aside.
In a large Dutch oven or other oven-safe pot, heat 2 tablespoons of the olive oil over medium heat. Add the rest of the chopped onion and sauté for 5 minutes, until tender. Stir in the garlic, and cook another 30 seconds. In batches, stir in the collard greens, stirring and letting each batch wilt before adding more. Stir in the tomato paste and water mixture, and season with salt. Add the cooked black-eyed peas, and pour in enough of the reserved cooking liquid to just cover everything. Place the pot in the oven, and cook for 30 minutes, until the collards and black-eyed peas are very tender.
Return the pot to the stovetop over medium-low heat. Add some more of the cooking liquid if it seems dry. Stir in the last tablespoon of olive oil and chopped dill. Cover, and simmer for an additional 10 minutes. Season with salt and pepper to taste. Serve hot, with lemon wedges.