In a large saucepan cook garlic in the 2 tablespoons hot oil over medium heat for 1 minute. Add onion and cook until tender. Add potatoes, chicken broth, and the water. Bring to boiling; reduce heat. Cook, covered, for 15 to 18 minutes or until potatoes are tender. Cool slightly.
Using a food processor or blender, puree soup in batches until smooth. Return to saucepan. Add slivered fennel and peas. Bring to boiling; reduce heat. Simmer, uncovered, for 3 minutes.
Stir in salt and pepper. Top each serving with fennel fronds. If desired, spoon yogurt onto each serving and drizzle with additional olive oil.