In a high-sided skillet or saucepan, melt the butter on medium heat. Then, add the flour and use a whisk to fully coat the flour with butter and make a smooth paste. Allow this to cook while stirring for 1 minute or more to cook off the flour taste.
Add about ½ cup of the broth while whisking fairly rapidly to dissolve the flour into the liquid. Once all or most of the flour paste is incorporated, add the remainder of the broth. Continue to gently whisk the gravy and bring it to a boil then lower the heat to a simmer.
Add the spices and stir them into the gravy. Cook for an additional 3 to 4 minutes. Taste the gravy and adjust the seasonings as desired. Serve hot.