Pre-heat oven to 500°F.
In a small bowl. mix together the butter, garlic, herbs, salt, and pepper until evenly combined.
Rub the herb butter all over the rib roast, then place on a roasting tray with a rack.
For medium-rare, take the weight of your rib eye roast and multiply it x 6 minutes; as an example, a 6-pound rib eye roast multiplied x 6 minutes = 36 minutes in the oven at 500°F.
For medium, take the weight of your rib eye roast and multiply it x 7 minutes; as an example, a 6-pound rib eye roast multiplied x 7 minutes = 42 minutes in the oven at 500°F.
Turnoff the heat and let the rib roast sit in the oven for 2 hours, making sure you do not open the oven door or else the residual heat will escape.
Once the 2 hours are up, remove the roast from the pan and pour the pan drippings into a saucepan over medium heat.
Add the flour, whisking until there are no lumps, then add the beef stock, stirring and bringing the sauce to a boil.
Remove from the heat and strain the sauce into a gravy dish.
Carve the prime rib into ¾-inch slices, pour a bit of Au Jus over the prime rib and serve.