Clean roast and pat dry. and Liberally season with coarse salt.

Leave uncovered on a sheet pan with a rack in the refrigerator overnight.

Pull the roast out to come to room temperature about 4 hours ahead of cooking

Preheat the oven to 500° F.

Combine butter, pepper, and herbes de Provence in a bowl; mix until well blended.

Spread butter mixture evenly over the entire roast. Season roast generously with kosher salt.

Place the roast into a roasting pan.

Roast the prime rib in the oven for 20 minutes for a 4 pound roast.

Turn the oven off and let the roast rest in the oven for 2 hours. DO NOT open the oven during this time.

Remove from the oven, allow to rest for about 15 minutes, slice, and serve with jus sauce if desired.

In a skillet add the drippings left from the roasting pan, and the onions, carrots, and celery over med-high heat. Cook until the veggies are slightly browned. Be sure to keep things moving and stir often to keep from burning.

Pour in 1.5 cups beef stock to release all of the fond (the bits on the bottom of the pan). If needed use a silicone spatula to get the rest of the bits off the bottom of the pan.

Transfer everything in the skillet to a large saucepan; add the remaining 1.5 cups of beef stock and simmer over low heat for about 20 minutes or until sauce has reduced by a third.

Strain veggies out using a mesh strainer.

Skim off any fat that rises to the top.

Add salt and pepper to taste.

If any other juices have leaked out of your roast while it has rested stir them into the sauce.

Serve with the sliced roast.