Place the mushrooms in a food processor and pulse until finely chopped. If you do not have a food processor, finely chop the mushrooms by hand.

Remove any resulting liquid from the mushrooms by placing them in a paper towel and gently squeezing.

Transfer the chopped mushrooms to a large plate.

Sprinkle the lamb loins all over with salt and pepper, then rub the mustard all over the loins, avoiding the ends.

Roll loins in the chopped mushrooms, pressing down gently to make sure the mushrooms adhere well.

Heat oil in a large skillet over medium high heat.

Add lamb and sear until brown on all sides, about 3 minutes per side.

Once seared, either reduce the heat to medium and continue to cook, covered, on the stove or transfer the uncovered skillet to a 350°F oven and continue to cook until a thermometer inserted into the center of the lamb reads 125°F for medium-rare, about 20 minutes, or longer if desired.

Remove the loins from the skillet and set them aside to rest for about 10 minutes.

Meanwhile, add wine, broth and sugar to the skillet and simmer on medium high heat until it reduces by about half, and is thick enough to coat the back of a spoon.

Slice each loin on a bias into eight slices.

Drizzle some sauce on the bottom of each plate and arrange four slices of lamb on top.

Top with thyme and serve.