Melt 1 tablespoon of the butter in a saucepan. Add the onion and thyme and cook over moderate heat, stirring, until the onion is translucent. Stir in the rice and cook for 2 minutes. Add the chicken stock and bring to a simmer. Reduce the heat to low, cover and cook, stirring, until tender, about 30 minutes for black rice and 45 minutes for wild rice. Season with salt and pepper.
Preheat the oven to 350° Spread the kosher salt in a roasting pan and set the shallots on top. Bake for about 45 minutes, or until tender. Let cool, then peel the shallots and trim the root ends. Raise the oven temperature to 450°.
Cut the lamb racks in half to form 4-chop racks. Season with salt and pepper and coat each rack with 1/2 tablespoon of the Chimichurri Sauce. Melt 1 tablespoon of the butter in the oil in an ovenproof skillet. Add the lamb racks, fat side down, and sear over high heat, turning once, until well browned all over, about 2 1/2 minutes per side.
Transfer the skillet to the oven with the racks fat side up and roast for about 10 minutes for medium-rare meat. Let rest for 5 minutes. Meanwhile, in a small skillet, melt the remaining 1/2 tablespoon butter. Add the roasted shallots and toss over moderately high heat until warmed through. Season with salt and pepper. Rewarm the rice.
Mound the rice on 4 large plates. Carve the racks and arrange the chops on the rice, garnishing each plate with the shallots and a drizzle of Chimichurri Sauce. Pass the remaining sauce separately.
The lamb, shallots and rice can stand at room temperature for 1 hour.
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