*Get as much pan drippings out of the roasting pan as you can. You may get the 1/2 cup or you may get more or less. Use enough beef stock to get 2 cups of stock and pan drippings combined. (So if you got 1/2 cup of drippings, use 1 1/2 cups of beef stock.)
You can prepare au jus while prime rib is resting.
Strain the pan drippings from the roasting pan into a measuring cup through a fine mesh strainer. (When getting the pan drippings out, make sure to scrape the bottom of the roasting pan (or foil) to get all the fond off. That's where a lot of flavor will be!)
Preheat the cooking pan over medium heat. Add butter and let it melt. Whisk in the flour and while you're whisking slowly, pour in the pan drippings.
Keep whisking and pour in the wine. Pour in the beef stock, still while whisking, and make sure that everything is mixed nice and smooth.
Taste and season the au jus with salt and pepper.
Bring it to simmer and lower the heat to medium-low. Let it simmer for about 15-20 minutes, stirring often. Take off heat when ready.
You can portion au jus into individual ramekins for serving or serve it in a sauce cup.