SOFTEN: Coat the bottom of a 4.5 quart dutch oven over medium low heat with the olive oil, then stir through the diced onion, carrots and celery. Cook, stirring here and there, until the vegetables begin to soften and the onion becomes translucent and shiny, a good 15 minutes. Stir in the minced garlic and cook until fragrant, another minute or so.
SIMMER: Nestle the pork hock(s) into the vegetables in the center of the dutch oven. Add the rinsed & picked split peas around the pork, then pour in the broth, which should just about cover the pork nicely. Increase the heat and cover the pan so that the broth comes to a near boil, then reduce the heat to a light, even simmer. Season with the black pepper & paprika, give the vegetables a stir, then re-cover the pot and let cook until the split peas are soft with a hint of bite left and the broth has become nice and creamy, about 45 minutes.
SHRED: Use tongs to remove the pork hock to a plate and allow to cool enough to handle. Taste the soup and see if it needs any additional salt, see notes. Break off the smoked pork from the hocks into bite size pieces and add back to the soup. Stir in the white wine vinegar. Remove and discard the bay leaves, warm through the pork and serve immediately. If however, you like a softer texture, more akin to a pureed soup, increase the cook time by a further 30 minutes before serving.
Using a lower sodium or unsalted broth allows you to better control the salt levels in this dish, since smoked ham hocks can vary greatly in their flavor and salinity. Let the soup simmer for at least 30 minutes before tasting and adding any additional salt, so that the ham hocks have time to release their retained salt.
When it comes to texture, everyone seems to like split pea soup on the creamy side, with varying degrees of doneness on the actual peas themselves. If you like a softer split pea, you can let the soup simmer a good hour or more. For a split pea that doesn’t, well, split and burst in the broth, you’ll want to keep the cook time closer to the forty five minute mark.
If you’re like me, you can cheat and keep some of the just-cooked-through peas from the pot, cook the brothy remainder for longer until super creamy, then add the reserved split peas back at the end before serving for some extra body. Make this pot your own, but I really do recommend that bright little splash of white wine vinegar at the end.