Preheat oven to 450 °F
In a food processor (or with handy knife skills), mince the parsley. Once finely chopped, combine with bread crumbs on a flat plate.
In a large saucepan, heat oil on high heat. Add the racks of lamb and get a nice sear on each side. 30 seconds to 1 minute per side.
Once all sides are seared, remove from pan and brush the tops of the rack (not the bone side) with the mustard, then press the rack into the parsley and crumb mixture. Return to pan, crumb side facing up and ribs facing down.
Place in oven for 15 minutes.
Remove from oven and check doneness with thermometer. Cover with aluminum foil and let stand for 10 minutes. (see pro tip for doneness)
While rack of lamb is resting, mince shallot and garlic.
On medium heat, using the same pan as the lamb, add butter to pan and sweat garlic and onion, 3-5 minutes scraping up brown bits from the bottom of the pan.
Add balsamic and bring sauce to a simmer for 2 minutes.
Slice lamb, serving 2-3 ribs per person. Drizzle a little sauce on each rib, serve hot!