In a large stockpot over medium heat, heat olive oil. Cook onion, carrot, celery and garlic until onion is translucent. Stir in yellow and green split peas, stock and bay leaf; season to taste. Cover, bring to a boil, then reduce heat and simmer 2 1/2 hours, stirring frequently.
Purée warm soup with a blender or food processor. Return to pot, heat through and serve.