For the Instant Pot:
Add the olive oil to the stainless steel inner pot of your Instant Pot. Set your Instant Pot to the saute function (low or medium setting), and add the leeks, celery, garlic, thyme, bay leaves and smoked paprika. Saute for 7-10 minutes, until the leeks are nicely softened, stirring often to prevent sticking or browning if you are using the higher setting. Add in a few generous grinds of black pepper, the washed split peas, and the broth. Stir well to make sure nothing is sticking to the bottom.
Secure the lid, with the pressure release valve set to “sealing”, and set your Instant Pot to cook on high pressure for 10 minutes.
Important note: Once your Instant Pot has completed its cooking time, DO NOT release the pressure manually (as this will put you at risk of releasing boiling hot liquid out of the pressure release valve). Let the pressure release naturally on its own, making sure the locking pin has released and no more pressure remains inside the pot before you unlock and remove the lid.
Once the soup is cooked and the pressure safely released, remove and discard the bay leaves and the thyme stalks. Either blend the soup while still hot in the stainless steel inner pot, by using a handheld stick blender, or decant the soup into an upright blender to puree when cooled. Puree thoroughly until completely creamy and liquid, adding a bit more broth if needed to adjust consistency.
Once the soup has been blended, add the lemon juice, and taste for seasoning, adding additional salt as desired. If you need to adjust the consistency of the soup, add in additional amounts of broth as needed.
Make sure to serve the soup piping hot, as pea soups have a tendency to form a skin on the top layer as they cool. Garnish with extra thyme leaves and a generous grind of black pepper. Enjoy!
For the Stovetop:
Follow the instructions as above, but instead of using the Instant Pot, use a heavy bottomed pot, such as a dutch oven. Once the initial ingredients are sauteed, and the broth and split peas added, bring to a boil and then lower to a simmer, cooking for approximately 30 minutes until your split peas are tender and falling apart, making sure to stir occasionally. Exact cooking time with dried beans always varies depending on the hardness and age of the batch you are using. Proceed to blend, and adjust final seasonings and garnish as above.