Heat olive oil in a large pot or Dutch oven over medium heat. Add onion, carrots, and celery and cook until softened, about 5-7 minutes.
Add garlic, thyme, and smoked paprika and cook for 1 minute more.
Add split peas and vegetable broth. Bring to a boil, then reduce heat and simmer for 30-40 minutes, or until the peas are tender and the soup has thickened.