In a large pot, heat olive oil over medium heat. Add onion, garlic, and broccoli and saut� for 5 to 7 minutes. Add the potatoes and chicken broth and bring to a boil. Simmer, covered, for 30 minutes or until potatoes are tender.
Use an immersion blender to blend the soup in the pot, or transfer it to a regular blender in batches to blend smooth. Do not fill the blender all the way to the top (liquid will be very hot!). Return the blended soup to the pot and stir in the frozen peas and yogurt.
Heat the soup for 5 to 10 minutes over medium heat, so that the peas soften. Garnish with additional peas, a dollop of yogurt, or a sprinkle of shredded cheddar cheese.