The basis of any "gravy" -- the western name for thickened brown sauce -- is a fat and a starch; mosts times butter with flour (a roux).
So, if you are avoiding either of these things, or limiting your fats/carbs, this may be something you want to learn more about.
Knowing whats IN our food and the process it goes through is half the battle.. especially if you aren't making it from scratch in your own kitchen.
If you were to make something at home, you could omit the roux and simply reduce the meat drippings to thicken a bit. This would give you the flavour without the addition of carbs and extra fat.