After soaking your beans overnight in salted water (which tenderizes them and seasons them from within), drain and rinse them thoroughly under cool water to remove the brine. Spread them on a clean surface and quickly inspect for any discolored or damaged beans, removing them as you find them. This preliminary cleaning ensures a uniform texture throughout your dish.

Heat 3 tablespoons of olive oil in a large, heavy-bottomed pot over medium-high heat. Add the diced salted pork and cook for about 4 minutes until it begins to brown, then add the ham hocks and continue cooking for another 10 minutes until the pork is crisp and the ham hocks are lightly browned, developing that essential smoky foundation. Remove both the pork and ham hocks to a plate, leaving about 2 tablespoons of the rendered fat in the pot—this flavorful fat is your base for the next phase. Add the diced onions to the same pot and cook for 7-10 minutes, stirring occasionally, until they soften and become translucent, then stir in the crushed red pepper flakes, cayenne pepper, bay leaves, smoked paprika, and a pinch of salt, cooking for about 30 seconds to bloom the spices.

Pour in the 1/2 cup of dry white wine, scraping the bottom of the pot with a wooden spoon to release all the caramelized bits stuck to the surface—these browned, flavorful bits (called fond) are liquid gold for building depth. Let the wine reduce for 2-3 minutes until slightly concentrated, then add the minced garlic and cook for just 30 seconds until fragrant. I like to add the garlic late in this process because it's delicate and can turn bitter if cooked too long, but those 30 seconds are enough to infuse its flavor into the oil.

Preheat your oven to 300 degrees. Return the ham hocks and pork to the pot, then add the 4 cups of chicken broth and 4 cups of water. Bring the mixture to a boil over medium-high heat, then add the prepared black-eyed peas and stir well. Once the liquid returns to a boil, cover the pot with a lid (or heavy-duty foil if you don't have one that fits) and transfer it to the preheated 300-degree oven. Braise for 1 hour—the gentle, consistent heat allows the beans to cook evenly and absorb all those developed flavors from the pork and aromatics.

Remove the pot from the oven and take out the ham hocks using tongs or a slotted spoon. Let them cool slightly, then pick all the meat from the bones, chop it into bite-sized pieces, and return it to the pot along with the bones (the bones add subtle flavor as the dish rests). Stir in the fresh thyme and cook the pot on the stovetop over medium heat for another 15 minutes. Next, ladle about 2 cups of the beans and broth into a blender (working in batches if needed) and puree until smooth, then stir this pureed mixture back into the pot—this creates a creamy, cohesive texture throughout the dish while keeping some whole beans for bite. Taste and adjust the seasoning with additional coarse sea salt and black pepper to your preference.

Ladle the black-eyed peas and broth into bowls, making sure each serving gets a generous portion of the creamy beans and flavorful broth. I like to remove the bay leaves before serving, though some people leave them in for presentation. Serve hot as a comforting main course or alongside cornbread, rice, or greens for a complete meal.