This soup is terrific for those of us watching our carb intake. It's flavorful and wonderfully creamy even though it contains absolutely no milk or cream. The soup is also great for ovo-lacto vegetarians with the cheese garnish and straight vegetarians by leaving the cheese out.
Heat oil in a large pot over medium heat; once the oil is hot, reduce heat to low. Cook and stir onion and garlic in hot oil until softened, 3 to 5 minutes. Add broccoli, season with salt and pepper, and stir. Pour vegetable broth and lemon juice into the pot.
Loosely cover the pot and simmer the mixture until the broccoli is tender, about 25 minutes. Puree with an immersion blender until smooth. Garnish with Cheddar cheese to serve.
If you don't have an immersion blender you can also use a traditional blender, but BE CAREFUL AND DO THIS IN SMALL BATCHES! The heat and steam could cause your blender's top to fly off and leave you burned and messy. I know this from experience with another soup.