Wash and chop broccoli. Dice the onion and mince the garlic.
Melt butter in a large pot or dutch oven over medium heat. Add the onion and cook for about a minute. Stir in the chopped broccoli and saute for 3-4 minutes, just until the broccoli turns bright green.
Add the flour and garlic, cook and stir for at least a minute, until the vegetables are evenly coated.
Add the broth, milk, and cream. Cook and stir with a flat edged spoon or spatula until bubbly.
Add the cubed Velveeta, pepper, and salt. Turn the heat to low heat and cook until the cheese melts, stirring often.
Taste and add more salt and pepper if desired.
Notes
We like our soup with a lot of broccoli, but you can use less if you prefer.
You can also add more cheese if you like a really rich and cheesy soup.