Heat oil in Dutch oven or soup pot over medium; cook onion, carrots, and celery about 8 minutes until softened.
Cook garlic another minute until fragrant; add paprika and thyme, stirring to coat.
Add peas, ham hock, broth, and bay; boil, reduce to low, and simmer partly covered about 90 minutes.
Stir occasionally to prevent sticking; cook until peas completely broken down and soup thickened.
Remove hock and bay; when hock cool enough to handle, shred meat and return to soup.
Season with salt and pepper; thin with broth or water if needed. Serve hot with crusty bread.