How to Make It
In each of 2 large heavy skillets, heat 1 tablespoon of the oil until almost smoking. Season the lamb chops with salt and pepper, add them to the pans and cook over high heat, turning once, until browned and crusty, 5 to 6 minutes. Transfer the lamb to a platter, cover loosely with foil and keep warm.
Add half of the shallots to each skillet and cook, stirring constantly, until softened, about 2 minutes. Add 1/4 cup of the wine to each pan and cook until almost completely reduced, scraping up any browned bits, about 5 minutes.
Scrape the shallot mixture into 1 skillet and add the tomato paste. Cook over high heat until beginning to brown, about 2 minutes. Add the demiglace and cook until reduced by half, about 8 minutes. Add the butter and swirl until it melts. Add any accumulated lamb juices and season with salt and pepper. Strain the sauce through a fine sieve into a bowl. Serve the lamb chops with the pan sauce.
Notes
Beef demiglace, a reduction made from thickened stock, is available at specialty food stores and by mail order from Dean & DeLuca (800-221-7714).