The Start - In a large pot, add the olive oil and heat to medium. Add the onion, garlic and leeks and cook until slightly soft, just 3-4 minutes.
Veggies - Add the potatoes, zucchini and broccoli and cook just 1-2 minutes and then add the broth. Add the bay leaf and cook until the vegetables are soft. About 20 minutes. Don't forget to keep that cup of broccoli and potato to finish off the soup.
Puree - Now I like to use my immersion blender, but you can also use a regular blender. You want to blend the soup until the mix is well pureed. Mix until you get a creamy and a smooth texture.
NOTE: Remove the bay leaf before you puree.
Add the remaining broccoli and potatoes and cook another 10 minutes until they get soft.
Finishing - Once the final broccoli and potatoes are soft add the herbs, and any seasoning like the salt and pepper along with the cheese and just heat up. This isn't a thick chowder but a nice creamy soup. It is really good and light with tons of flavor.
NOTE: If you like it thicker, you can mix a little corn starch with some water to make a slurry and then add to the soup (just 1 tablespoon of each) and bring the soup to medium boil and it will thicken. For me - I don't think it needs any thickening. But you can add that if you want.
My touch - I love to serve this with a tomato I just roasted in the oven topped with olive oil and bread crumbs. Simply on a piece of foil. 10 minutes as the soup was finishing up. It is just the perfect finish. I used just a light drizzle of olive oil and then dredged in Italian dried bread crumbs. Roast at 425F for 10 minutes is all.