Preheat oven to 450°F.
Starting with the soup base, in a 3 - 4 quart heavy based pot or dutch oven, over medium heat, add 2 Tbls Butter and melt.
Once butter is melted, add in the Onions and finely diced Potatoes and saute until the onions are starting to turn translucent. Cook for about 8 - 10 minutes, stirring occasionally and cook until just potatoes are tender.
It's time to pour in the Chicken Broth and add in the Broccoli florets bringing to a boil, after about a minute turn down heat to low and simmer for 15 minutes.
For the Blonde Roux, over low heat in a medium to large skillet, completely melt the 4 Tbls of Butter.
Once the butter is melted, then add in the Flour 1 Tbls at a time, stirring in between to make sure there are no lumps.
Keep stirring the Roux slowly until there is a nutty aroma, about 3 - 5 minutes.
Just before taking off the heat, add in the Nutmeg and blend well. Remove from heat and set aside.
To make the Parmesan Croutons, on a baking sheet, place the bread croutons in a single layer. Toast the bread in the preheated 450°F oven for about 5 minutes.
Remove croutons from oven and sprinkle the Parmesan cheese all over the bread. Return croutons back to the oven and continue to toast/bake for an additional 3 - 5 minutes or until cheese is melted and bread is starting to turn golden.
For the soup, once the Broccoli is a vibrant green, stir in the Blonde Roux mixing in well. When the Roux is blended in well, add in the Heavy Cream or Half and Half heating through for a couple of minutes.
Remove from heat and add to blender in batches and pulse blender until soup is creamy and smooth. You can also use a handheld blender straight in the pot you were cooking in (my favorite way), and blitz until creamy and there are no more big bits of potato or broccoli. (*Note: If you would like your soup on the chunkier side, simply set aside about 1/3 of your soup and then just blitz the remaining soup until creamy and smooth. Once you have desired consistency, return the chunkier soup to the blended soup and stir together until well incorporated.
Taste and season with Salt and Pepper. If needed a pinch or two more of Nutmeg as well. Taste again to make sure it's seasoned well.
Serve soup with the Parmesan Croutons and Enjoy immensely!