Heat olive oil in a large Dutch oven or soup pot over medium heat. Add the onion, carrots, and celery, cooking until softened, about 8 minutes.
Stir in the garlic and cook for another minute until fragrant. Add the smoked paprika and thyme, stirring to coat the vegetables.
Add the split peas, ham hock, chicken broth, and bay leaves. Bring to a boil, then reduce heat to low and simmer, partially covered, for about 90 minutes.
Stir occasionally to prevent sticking. The soup is ready when the peas have completely broken down and the soup has thickened.
Remove the ham hock and bay leaves. Once the ham hock is cool enough to handle, shred the meat and return it to the soup.
Season with salt and pepper to taste. If the soup is too thick, add a bit more broth or water to reach your desired consistency. Serve hot with crusty bread.