Warm a saucepan or cast-iron skillet for 2 minutes over medium heat.
Melt the butter or other solid fat, if using. If not, add the oil to the skillet.
If using butter, do not let it brown.
If using oil, heat it for another 2 minutes.
Add the flour and whisk constantly.
Whisk another 6 -8 minutes, or until the roux is smooth and has a light golden color. Watch out for burning.
You can make roux ahead to store. Transfer the made roux to a heatproof bowl and stir it to cool down quickly.
Store in the refrigerator for 2 months, or up to 6 months in the freezer.
To freeze roux, spoon 1 tablespoon into each section of an ice cube tray.
Use 1 or 2 cubes to thicken a sauce, soup, or stew; or use 8 cubes to make ½ cup.
Another thickener is cornstarch or potato starch. Mix 1 tablespoon of either starch with 1 cup of cold water and stir to avoid separation.
Add this starchy slurry to the hot gravy, soup, or stew, slowly and only 1 tablespoon at a time. Stir constantly. You may need only a few tablespoons to obtain a thicker sauce.