Standard Recipe Disclaimer: I am not big on measuring, use your best judgement.
Peel and dice potatoes. I used 5 good size russets, whatever you have will work. I'd guess maybe 6 cups of diced potatoes, somewhere around there. In a stock pot or dutch oven, throw in some butter, maybe a few tablespoons. Toss in the onions and cook several minutes until they start to turn translucent. Add minced garlic, a few teaspoons should do it, and cook a few more minutes. Toss in the potatoes, and stir around to coat and cook for a few minutes.
Add enough stock to completely cover the potatoes. If you want to be cool, and I know you do, add a little bag of fresh herbs like rosemary, basil, thyme, and tarragon. Oh yeah. Simmer until potatoes are nice and mushy, or at least as mushy as you like them, maybe 30 minutes.
In another pot, throw in about 4 tablespoons of butter and melt. Add in 4 tablespoons of flour and whisk. Cook a few minutes, the roux should thicken up nicely. Whisk in some heavy cream, I used a pint. Bring to a boil while whisking constantly.
Add the roux/cream to the soup and stir in in well. Taste it. Add salt and pepper until it tastes good. I added some old bay seasoning, and that was a good idea. Now add in a package of shredded cheddar cheese. Add in some broccoli, maybe 1 head or more if you like broccoli, just remember to wash it first like I always forget to do. Simmer all this for a bit, maybe 10 minutes, until the broccoli is cooked enough for you. If you want, take a stick blender and smooth things up a bit, but I didn't.
DONE! Makes about 10 servings of seriously thick and creamy soup.