Prep the lamb. Take the lamb out of the refrigerator about 10 to 15 minutes before cooking. Pat dry, then season all over with 1 teaspoon salt and ½ teaspoon black pepper.
Make the mustard mixture. In a small bowl, stir together the Dijon mustard, honey, and dried tarragon. Set aside.
Make the mint crust. Bring a small pot of water to a boil. Blanch the mint leaves for about 10 seconds, then transfer immediately to ice water. Once cooled, squeeze out as much water as possible and pat dry.
Add the mint to a food processor with the breadcrumbs, remaining 1 teaspoon salt, remaining ½ teaspoon black pepper, cayenne, and olive oil. Pulse until the mint is finely chopped and mixed throughout. Add the Parmesan and pulse just until combined. Transfer the mixture to a shallow plate.
Sear the lamb. Preheat oven to 400°F. Heat a cast iron skillet over high heat and add the grape seed oil. Once hot, sear the lamb until browned on all sides. Leave the racks whole if your skillet fits them. Otherwise, cut them in half or work in batches.
Roast until nearly done. Place the lamb in the skillet fat side down, rib side up. Transfer to the oven and roast until the lamb is about 15 to 20 degrees below your final target temperature.
For smaller racks, start checking around the 5 to 7 minute mark. For medium-rare, look for around 105 to 110°F before the crust goes on. Larger racks will take longer.
Add the mustard and crust. Remove the lamb from the oven and increase the oven temperature to 450°F.
Brush the mustard mixture generously over the meaty parts of the lamb, avoiding the exposed rib bones. Press the mint-breadcrumb mixture firmly onto the lamb until well coated.
Finish at high heat. Return the lamb to the skillet, rib side down and crust side up. Roast at 450°F until the crust is set and the lamb reaches your preferred doneness.
For medium-rare, pull the lamb when the thickest part reaches about 125 to 130°F. The temperature will continue to rise as it rests.
Rest and slice. Let the lamb rest for 10 minutes before slicing between the bones into chops.