The night before, place the black-eyed peas in a large bowl and fill it with cool water (there should be at least three times as much water as dried peas). Soak them overnight in the refrigerator.
Heat a medium-sized skillet over medium heat. Add the bacon and cook until crisp, turning occasionally for 5-7 minutes. Transfer the bacon to a paper-towel-lined plate to absorb the grease.
Drain the excess bacon fat from the skillet, leaving about a tablespoon for flavor. Add the olive oil and heat on medium-low. When the oil is hot, add the onions, garlic, celery, and thyme. Sauté for 3-5 minutes until vegetables begin to soften and are fragrant.
Next, drain the soaked peas in a colander and rinse them under cool tap water. Add the rinsed peas to the pot with the vegetables, followed by the paprika, bay leaf, cayenne pepper (if using), and chicken broth. Mix well—season with salt and pepper to taste.
Cover the pot with a lid, turn the heat to high, and bring the water to a boil. Once it boils, turn the heat down to low and simmer for 60-80 minutes.
After one hour of simmering, the black-eyed peas should be tender. Add the collard greens to the pot and stir them in until wilted. Smash some of the peas against the side of the pot as you stir to help thicken the liquid if desired. If the soup is too thick, add a little broth or water ¼ cup at a time until it reaches your desired consistency.
Bring the pot back to a low boil and simmer the peas and greens for an additional 15-30 minutes (depending on how tender you like your greens). It's done when the greens are tender, and the peas have broken down further, thickening the liquid even more.
Taste the peas and add salt to your liking (I used about a teaspoon of salt for this recipe). Serve with bread, rice, or cornbread, and enjoy!