Melt butter in a skillet or pan.
Once the butter is melted and bubbly, add your flour two tablespoons at a time.
Whisk the flour into the butter very well in between each flour addition.
Once all of the flour has been added to the butter, stir the clumpy butter/flour mixture around your pan. This will cook out the flour flavor.
Slowly add your broth a little at a time, whisking constantly.
Slowly add your milk a little at a time, whisking constantly.
Add your salt, pepper, and any other desired seasonings.
Continue to cook your cream of chicken soup, stirring constantly, until it reaches the thickness you desire.