I'll have to try making the rue from butter and flour.
When I cook a chicken or piece of beef, I put stock in the pan. Then before serving, I strain most of the stock out, and mix some of the cooled stock with corn starch to make a paste. If I don't let it cool enough, I get lumps. I stir that back into the rest of the stock and heat till it thickens.
If it's not thick enough, I put some more corn starch in a little strainer, and shake over the gravy while stirring.
If I want more flavour, I'll add bullion powder, and I usually add some browning and seasoning liquid.