In a large saucepan, heat oil over medium heat. Add onion and celery. Cook, stirring often, for 7 minutes. Add garlic and pepper. Cook, stirring, for 30 seconds. Add broth, 1/2 cup water, carrots, peas, and bay leaf. Bring to a boil, reduce heat, cover, and simmer until peas are tender, about 1 hour.

Remove from heat and cool for 10 minutes. Remove carrots and bay leaf. Cool carrots slightly, chop into bite-size pieces, then set aside.

In a blender or food processor, puree cooled soup in batches until smooth.

Pour mixture back into saucepan and heat through.

In a small bowl, whisk 1 cup hot soup into yogurt until blended. Whisk mixture back into remaining soup in saucepan and heat through.

Stir in carrots and serve immediately.