Heat olive oil in a large pot over medium heat.
Add diced onion and cook until softened, about 5 minutes.
Stir in minced garlic and cook for an additional minute.
Add chopped broccoli and vegetable broth to the pot, bringing to a boil.
Reduce heat and let the mixture simmer for about 10 minutes.
In a separate pot, cook the shell pasta according to package instructions.
Once the broccoli is tender, use an immersion blender to puree the soup until smooth.
Stir in the heavy cream and shredded cheddar cheese, mixing until smooth and melted.
Add salt and pepper to taste, and adjust the seasoning as needed.
Finally, add the cooked shell pasta to the soup, stirring well to combine.
