I make this ever so often.
Wish I had read this before defrosting chicken for today! :)
I cheat and use my blender to make the thick white sauce. But I'll tell you how I make mine.

Hamburger Gravy

I brown very lean hamburger. (No need to drain it.) I add onions, salt and pepper.

Then in my blender I use 6-8 T. of butter, and 6-8 T. of flour & 2 C. milk.I "whip" until blended, then pour into
the hamburger pan,stirring while adding, and cook over low heat, stirring until thick. Season to taste
with salt & pepper. I usually add 1-3 C. more milk to
the pan for making more gravy. Trick is to simmer to cook out the flour taste.

My Mom used to fix this at least once a week.