Rinse the dried split peas thoroughly in a colander under cold water and remove any stones or debris.

In a large Dutch oven or soup pot, heat the olive oil over medium heat, then add the chopped onion, carrots, and celery.

Sauté the vegetable mixture for about 5 to 7 minutes until the onions turn translucent and the carrots begin to soften.

Stir in the minced garlic and cook for another minute until fragrant, being careful not to let it brown too much.

Add the rinsed split peas, smoked ham hock, chicken broth, bay leaves, dried thyme, and smoked paprika to the pot.

Increase the heat to bring the soup to a boil, then reduce the heat to low, cover, and let it simmer gently.

Cook for 60 to 80 minutes, stirring occasionally, until the peas have completely broken down and the soup has thickened.

Carefully remove the hot ham hock from the pot and set it aside on a cutting board to cool slightly.

Check the consistency of the soup; if it is too thick, stir in a small amount of water or extra broth to reach your desired texture.

Pull the meat from the ham hock bone, chop it into bite-sized pieces, and discard the bone, skin, and excess fat.

Return the chopped ham to the soup pot and stir well to combine, letting it heat through for a few minutes.

Taste the soup and season with freshly ground black pepper and salt if needed, keeping in mind the saltiness of the ham.

Remove and discard the bay leaves before ladling the hot soup into bowls to serve immediately.