Roast Prime Rib:

Preheat the oven to 500 degrees.

Place the celery, onions, and carrots in the bottom of a roasting pan. Stir in the garlic, bay leaf, and olive oil, stirring until the vegetables are nicely coated.

Generously season the roast with salt and pepper and place it on top of the seasoned vegetables. Place in the preheated oven and roast for 15 minutes, or just until the meat is beginning to brown.

Lower the heat to 425 degrees and continue roasting for 30 minutes (or perhaps a bit longer), or until an instant-read thermometer inserted into the center reads 120 degrees for rare.

Remove from the oven and allow the meat to rest for 15 minutes. Remove and discard the bay leaf.

Carve the meat at the table and serve with a wedge of Gratin Potato and the roasted vegetables.

Gratin Potato:

Preheat the oven to 375 degrees.

Lightly coat a 10-inch-oval casserole dish with the softened butter. Set aside.

Combine the chervil, thyme, tarragon, and chives in a small bowl. Set aside.

Combine the cream and garlic purée with salt and pepper to taste in a medium saucepan over medium heat. Bring the mixture to a boil and immediately remove from the heat. Keep warm.

Peel the potatoes and cut them lengthwise into ¼-inch-thick slices on a mandoline or Japanese vegetable slicer. Ladle ½ cup of the warm cream mixture into the bottom of the prepared casserole.

Working quickly, make a ring of slightly overlapping potato slices around the perimeter of the prepared casserole. Continue making slightly overlapping potato rings until the bottom of the dish is entirely covered with potatoes. Lightly season the top with salt and pepper.

Sprinkle 1 tablespoon of the reserved herb mixture over the seasoning.

Using 1 cup of the grated Gruyère, make a thin layer of cheese over the potatoes. Ladle 1 cup of cream over all of it.

Continue making layers of potatoes, seasoning, herbs, cheese, and the cream mixture until you have made 3 additional layers. Finish with a layer of Parmesan.

Cover the entire casserole with aluminum foil and place in the preheated oven. Bake, covered, for 1 hour, or until a toothpick is easily inserted into the center.

Remove the foil and bake for an additional 10 minutes, or until the top is golden brown.

Remove the gratin from the oven and allow to rest for 15 minutes to firm up before cutting into serving pieces.