Melt the butter in a medium heavy-bottomed Dutch oven or pot over medium heat. When the butter has begun to bubble, sprinkle in the flour and whisk continuously until fully mixed. Continue to cook, whisking often, until the roux smells toasty and is the color of peanut butter, 4 to 6 minutes.
Carefully pour in 3 cups stock, whisking constantly, until fully incorporated, making sure to whisk in the corners of the pot. Raise the heat slightly and bring to a boil, whisking often, about 3 minutes. Lower the heat and simmer, uncovered, whisking occasionally, until thick and glossy, 10 to 15 minutes. (The gravy will be very thick at this point.)
Set aside until ready to use, up to 4 hours, or refrigerate overnight.
To reheat: Heat the gravy in a heavy-bottomed pot over medium heat, whisking often, until warm. Whisk in 1 cup of additional liquid, using drippings, stock or a combination of the two, until the desired consistency is reached. Whisk in the additional liquid gradually, stirring after each addition.
To finish: Whisk in the mustard and taste for seasoning. Add salt and pepper to taste, being careful to avoid oversalting.