In a large pot over medium heat, add olive oil and butter until melted. Add in chopped onion and garlic and sauté for 2 minutes.

Add the chopped broccoli stems, chopped potato, season with salt and pepper and sauté for 4-5 minutes.

Add stock and water, bring to a light boil, stir, and then reduce the heat to a simmer and cook partially covered for about 10 minutes (or until stems and potato are softened when you pierce a knife through).

Carefully blend the soup using a blender or an immersion blender (if using a blender do this in batches). Once blended, add the soup back to the large pot and bring back to a simmer.

Add in the medium size pasta shells and cook according to package instructions (note that it may take longer since you're cooking on a lower heat and not in boiling water).

Once the shells are al dente, add in the very finely chopped broccoli florets. These will cook very quickly (roughly 3-4 minutes), continue to stir.

Turn the heat off, add in heavy cream and grated cheddar cheese. Stir well to combine and serve. Option to add more grated cheese at the end!