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Roast Prime Rib:
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Preheat the oven to 500 degrees.
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Place the celery, onions, and carrots in the bottom of a roasting pan.
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Stir in the garlic, bay leaf, and olive oil, stirring until the vegetables are nicely coated.
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Generously season the roast with salt and pepper and place it on top of the seasoned vegetables.
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Place in the preheated oven and roast for 15 minutes, or just until the meat is beginning to brown.
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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.
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Remove from the oven and allow the meat to rest for 15 minutes.
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Remove and discard the bay leaf.
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Carve the meat at the table and serve with a wedge of Gratin Potato and the roasted vegetables.
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Gratin Potato:
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Preheat the oven to 375 degrees.
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Lightly coat a 10-inch-oval casserole dish with the softened butter.
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Set aside.
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Combine the chervil, thyme, tarragon, and chives in a small bowl.
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Set aside.
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Combine the cream and garlic puree with salt and pepper to taste in a medium saucepan over medium heat.
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Bring the mixture to a boil and immediately remove from the heat.
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Keep warm.
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Peel the potatoes and cut them lengthwise into 1/4-inch-thick slices on a mandoline or Japanese vegetable slicer.
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Ladle 1/2 cup of the warm cream mixture into the bottom of the prepared casserole.
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Working quickly, make a ring of slightly overlapping potato slices around the perimeter of the prepared casserole.
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Continue making slightly overlapping potato rings until the bottom of the dish is entirely covered with potatoes.
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Lightly season the top with salt and pepper.
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Sprinkle 1 tablespoon of the reserved herb mixture over the seasoning.
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Using 1 cup of the grated Gruyere, make a thin layer of cheese over the potatoes.
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Ladle 1 cup of cream over all of it.
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Continue making layers of potatoes, seasoning, herbs, cheese, and the cream mixture until you have made 3 additional layers.
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Finish with a layer of Parmesan.
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Cover the entire casserole with aluminum foil and place in the preheated oven.
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Bake, covered, for 1 hour, or until a toothpick is easily inserted into the center.
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Remove the foil and bake for an additional 10 minutes, or until the top is golden brown.
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Remove the gratin from the oven and allow to rest for 15 minutes to firm up before cutting into serving pieces.
