1. Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant.

2. Stir in the broccoli florets and vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover the pot and cook for 10-12 minutes, or until the broccoli is tender when pierced with a fork.

3. Carefully transfer about half of the soup to a blender and blend until smooth. Alternatively, use an immersion blender directly in the pot until you reach your desired consistency. Return the blended portion to the pot if you used a regular blender.

4. Reduce the heat to low. Stir in the milk, heavy cream, shredded cheddar cheese, and grated Parmesan cheese. Cook, stirring constantly, until the cheeses are fully melted and the soup is creamy and smooth. Do not let the soup boil after adding the dairy, as it can curdle.

5. Remove the pot from the heat. Stir in the fresh lemon juice, salt, black pepper, and optional pinch of nutmeg. Taste and adjust seasonings as needed.

6. Ladle the creamy broccoli lemon soup into bowls and serve immediately.