In a large saucepan, heat the butter until melted, then cook the onions until softened.
Add the garlic, and cook 30 seconds more, then remove onions/garlic and set aside.
Add the second amount of butter to the saucepan, melt, then blend the flour in with a whisk.
Whisk in the half & half, then add the chicken stock.
Simmer (do not boil) until thickened.
Add the broccoli, cooked onions/garlic, and simmer over low heat until the broccoli is tender, but still bright green.
Season to taste.
Remove from heat and puree all or half (if you like it chunky) in a blender.
Return to heat, and stir in the cheddar.
Serve, with extra cheese on the top.
Then, get a second bowl after you ate the first.
Notes
You may like to add shredded carrots at the same time as the broccoli if you are going for a full copycat of Panera's Broccoli Cheddar Soup!Want to use homemade chicken stock? Check out my recipe for how to make chicken stock!