Standing Rib Roast with Aioli
['1 shoulder-end 4-bone standing beef rib-eye roast, preferably dry-aged (about 8 pounds), chine bone removed', 'Kosher salt, freshly ground pepper', '2 large egg yolks', '2 garlic cloves, finely grated', '1/2 cup grapeseed or vegetable oil', '1 tablespoon fresh lemon juice', '1/2 cup extra-virgin olive oil']
Generously season beef with salt and pepper. Wrap tightly in plastic and chill at least 1 day.
Let beef sit at room temperature 2 hours.
Preheat oven to 400°F. Place beef on a rack set inside a roasting pan. Roast until nicely browned, 35–40 minutes. Reduce oven temperature to 275°F and continue roasting until an instant-read thermometer inserted into the thickest part of beef registers 115°F for medium-rare, 1–1 1/2 hours longer. Transfer roast to a cutting board with ribs pointing upward and let rest at least 30 minutes.
Meanwhile, whisk egg yolks and garlic in a medium bowl. Whisking constantly, gradually add grapeseed oil, drop by drop at first, and whisk, adding 1 tablespoon lemon juice by the teaspoonful as aioli thickens (juice will thin aioli so it's easier to whisk), until it is thickened and smooth. Gradually whisk in olive oil, adding water by the teaspoonful if aioli gets too thick. Season with salt; cover and chill.
Cut meat off bones, following curve of ribs, and thinly slice. Or, cut between ribs into massive chops for sharing. Serve with aioli.
DO AHEAD: Rib roast can be seasoned 2 days ahead; keep chilled. Aioli can be made 1 day ahead; keep chilled.
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