In a large pot over medium heat, melt butter. Add in onions, celery, carrots, and garlic cook to soften about 5 minutes.
Whisk in flour and cook another 30 seconds.
Add in chicken stock, milk, heavy cream, and broccoli and whisk until combined. Simmer on medium-low until thickened about 8-10 minutes, stirring occasionally.
Once thickened turn off the heat and add in the cheese and nutmeg. Whisk until melted and smooth.
Let stand for 5-10 minutes to cool and the soup will thicken more.
Serve with crispy bread slices or crackers.
Video
Notes
I use whole milk and heavy cream, but you could use half and half if you want.Always shred your own cheese. Pre-shredded cheeses contain potato starch and don't melt as nicely.Serve this homemade broccoli cheddar soup with some crusty bread like Ciabatta Garlic Bread, breadsticks, or some homemade Artisan Bread.You can freeze any leftovers in freezable containers if desired.