In a large soup pot or Dutch oven over medium high heat, heat the olive oil. Add the onion and carrots and saute for 2 minutes. Add garlic and split peas and saute for 1 minute.
Add the vegetable broth. Bring to a boil, then simmer for 45 to 55 minutes, until the split peas fall apart and the soup becomes thickened. If you’d like, with a hand-held immersion blender, pulse a few times to yield a smoother yet still chunky texture.
Stir in the liquid smoke, kosher salt, and fresh ground pepper. Garnish with smoked paprika if desired.