Broccoli Potato Cheese Soup

We adopted a new dining lifestyle recently and it's caused me to stretch myself and try to prep new things. This was one of my first adventures, and it was delicious. I like my veggies to be large in a soup, like a button on a pair of jeans, but it's entirely up to you.  (bigger is less work).

Ingredients
1 white onion, diced
4-5  small or 2-3 large carrots, diced
5-6 yukon gold potatoes, diced (you can peel them or leave skins on)
4-5 cloves minced garlic
1 qt boxed stock (veggie or chicken) - I like Kitchen Basics brand best
1 large head or 2 small fresh broccoli, chopped into bite size pieces, keep the crumby bits, not the stalks
6 tbsp butter
3-1/2 c whole milk*** see tip below***
4 c (2 bags) shredded cheddar cheese
1/3 c flour
salt
pepper
tabasco/sriracha

Non-standard supplies
none

Instructions
1. In a large pot, melt 2 tbsp of the butter and add the onion and carrot and cook over medium heat for about 5 minutes until the onions are soft and carrots sweat..
2. Add the garlic and stir it, but don't brown it. Just a few seconds.
3. Add the potatoes and stock. Bring to a boil.
4. Let it boil about 10 minutes so the potatoes and carrots become fork-tender. Then add the broccoli and reduce heat to a simmer.

While that's doing it's thing...  in a large saucepan:

a) Over medium heat melt, but do not brown the remaining 4 tbsp of butter. it MUST be real butter.
b) stir in the flour with a wooden spoon and it'll form a dough ball. keep stirring it for 3-4 minutes until this roux is turning a golden color - there should be no visible flour, just a thick doughy batter.
c) add the milk and stir until the dough ball is fully incorporated into the milk, which will thicken
d) add the cheese and stir until it's all melted and gooey. It'll look like a beautiful cheese sauce and you'll think it's too thick for soup.  (that's a good sign)
e) add salt pepper and sriracha to taste
f) once it's delicious to you and smooth, put the cheese sauce into the simmering veggies and stir to blend
g) taste, add salt and or pepper if needed, and eat up!

Variations
I don't keep whole milk on hand. We drink 2% typically, so I bought a pint of heavy cream and supplemented the rest with the 2%

You could certainly top this with crumbled bacon and  or green onion slices

You could use half cheddar and half another (cojack or pepperjack). I'd suggest leaving out the sriracha if you used pepperjack.