Broccoli and Cheese Soup (with Green Chile)

My Broccoli and Cheese Soup has a lot of green chiles in it which I LOVE.  I am not a big soup eater, but when I choose soup this usually on the list.  I am even happier if I have some good crusty peasant bread or sourdough to go with it.  The best is taking this with you in a thermos on a hike in the cold or when you have a sinus issue going on as I often do.  So, leave out the chiles if you like, but I want 'em. 

Broccoli and Cheese Soup

1 whole sweet yellow onion chopped
1 stick (1/2 C) butter (I used unsalted in this recipe so I can regulate the salt content in the soup, but whatever you'd prefer)
1/3 C flour (use more if you want this extra thick or less depending on your preference)
4 C milk (I use whole with this recipe, but 2% would work just won't be as creamy)
2 C half and half (or heavy cream)
Approximately 4 heads of fresh Broccoli chopped however you'd like
About 3/4 C of 505 Roasted medium green chiles (if you cannot find these in the jar next to the salsas ten go with one small can of hot chopped green chiles, it will taste a little different, but still pretty good)
3 1/2 C cheese, shredded fresh (I use monteray jack and sharp white cheddar mixed)

Sea salt and black pepper to taste

Melt the butter in a pan ( I do this all in a large saucepan) on medium heat and toss in the chopped onion.  One the onion is turning clear (translucent) throw in the flour and stir until combined and keep stirring for about another minute.  Add the milk and, half and half and a tad bit of salt and pepper along with the broccoli and green chiles.  Stir this all together well then let it come up to a small boil and let it simmer for about a half hour.  Then add the cheese and stir it until all the cheese melts.  I prefer my soup chunky, but if you so choose this soup can easily be pureed in a blender.  Also I have made this recipe in the slow cooker.  When doing this in the slow cooker do not skip the onion frying step and do not put in the cheese until a half hour before shutting off the crock-pot.  I did this 4 hrs on low.