pattern. Season generously with spice rub, and store them in the refrigerator, 1 hour to overnight.
Preheat the oven to 375°F. Before cooking the lamb, let the rack come to room temperature, about 10 minutes. Season the lamb with salt, to taste. Heat a large cast-iron or skillet pan over medium heat. Add the canola oil, and place the racks of lamb fat cap down. Slowly roast and render the fat cap first. When they are golden brown, flip the lamb to the other side, and sear all sides until golden, about 2 to 3 minutes per side.
When the lamb rack is finished searing, put the butter and thyme in the pan. Baste the lamb with the brown butter. Leave the rack of lamb in the pan with the fat cap on top and bone on the bottom. Put this pan of lamb in the oven on the middle rack, and finish cooking for 10 minutes. When the internal temperature reaches 130°F, the lamb will be about medium. Remove from the oven and rest the lamb rack for 5 minutes, then slice and plate.
To plate, spread the sesame sauce on the bottom, arrange the lamb chops with the roasted shallots and garnish with finishing salt on top.
Beijing Spice Rub
Toast each spice in a small sauté pan over high heat for about 2 minutes. When you can smell the spices in the air, they are ready. Grind them separately into powders with a spice or coffee grinder. Then sieve the spice powders, and combine them together to make Beijing spice rub.
Preheat the oven to 400°F.
Clean and peel the shallots. Put them in a mixing bowl, and toss them with the thyme, garlic and olive oil. Season with salt and pepper. Roast them in a 400°F oven for about 15 minutes; the shallots should be tender. After removing the shallots from the oven, cover the roasting pan with plastic, and hold them warm in their own juice.
In a heavy-bottom mixing bowl, combine the sesame paste and water, stirring in one direction and slowly emulsifying the paste and water. If you have a heavy-duty blender, you can also blend this mixture until smooth.
Place the soy sauce and minced garlic in a soup bowl. Heat up the canola oil in a small sauté pan over high heat and when the oil is smoking, place the Sichuan peppercorns into the hot oil. Be careful of the oil popping; don’t get burned. After about 30 seconds, when the aroma of the Sichuan peppercorns fills the air, remove the pan from the heat and immediately pour this Sichuan peppercorn–infused hot oil through a small strainer into the soy sauce bowl. The hot oil will flash cook the garlic soy sauce.
Pour this soy sauce–hot oil mixture into the sesame sauce, add the vinegar and mix well. Adjust the seasoning with salt to your liking. You can keep this in the refrigerator for up to 1 week.
Heat up a small sauté pan over high heat. Put the sesame seeds and coarse sea salt in the pan, and toss the pan to mix these 2 ingredients together while toasting, about 2 minutes.