Rinse the split peas thoroughly under cold water in a fine-mesh sieve and set aside.
In a large heavy-bottomed pot, heat the olive oil over medium heat and add the diced onion, carrots, and celery.
Sauté the vegetables for 5-7 minutes, stirring frequently, until the onions are translucent and the carrots begin to soften.
Stir in the diced ham and smoked paprika, cooking for another 2 minutes to lightly brown the ham and release the smoky aroma.
Add the rinsed split peas, chicken broth, sea salt, black pepper, and the bay leaf to the pot.
Bring the mixture to a boil, then immediately reduce the heat to low and cover the pot with a tight-fitting lid.
Simmer for 45-60 minutes, stirring occasionally to prevent sticking, until the peas have broken down and the soup has reached a thick, creamy consistency.
Remove the bay leaf before serving and adjust seasoning with additional salt or pepper if desired.