In a large pot, heat oil over medium heat. Sauté onion, garlic, asparagus and broccoli until fragrant (about 5 minutes). Cover with broth, add potatoes and bring to a boil.
Reduce heat to medium-low and simmer gently until vegetables are tender, 15 to 20 minutes. Remove pot from heat and set aside to let cool slightly.
Carefully transfer soup to a blender (in batches) and purée until smooth. Now season with lemon juice, salt and pepper. Ladle the soup into bowls, add a squeeze of lemon, fresh ground black pepper and a drizzle with olive oil if desired. Enjoy!
