How to Make It
In a medium saucepan, melt 1 tablespoon of the butter in the olive oil. Add the chopped shallots and cook over high heat, stirring a few times, until richly browned, about 5 minutes. Add the beef stock, red wine and thyme leaves and boil over high heat until reduced to 1 cup, about 10 minutes. Strain the shallot jus into a small saucepan. Whisk in the remaining 4 tablespoons of butter, 1 tablespoon at a time. Season with salt and pepper.
Preheat the oven to 400°. Season the lamb with salt and pepper. In a large ovenproof skillet, heat 1 tablespoon of the vegetable oil until shimmering. Add the lamb fat side down, and cook over moderately high heat, turning once, until browned all over, about 8 minutes.
Transfer the lamb to a large plate and let stand for 10 minutes. Using a mortar and pestle or spice grinder, coarsely crush the coriander seeds. Spread the coriander on a plate. Rub the lamb all over with the coriander, pressing to adhere.
Pour off any fat in the skillet. Add the remaining 1 tablespoon of vegetable oil and heat until shimmering. Set the lamb in the skillet, fat side down, and transfer the skillet to the oven. Roast for about 22 minutes, turning the lamb halfway through, until the meat is medium-rare and an instant-read thermometer inserted in the thickest part registers 125°. Transfer the lamb to a carving board and let rest for 10 minutes.
Gently reheat the jus, stirring, until hot; do not let it boil. Cut the rack between the ribs and arrange the chops on plates. Serve, passing the shallot jus at the table.