Preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper. Season the lamb rack on all sides with 1 tablespoon of Emeril's Creole Seasoning; set aside.
In a small bowl, combine the breadcrumbs, remaining 1/2 teaspoon Emeril's Creole Seasoning, the rosemary, and oil, and mix until all the crumbs are moist. Set aside.
Heat a 14-inch skillet over medium heat until hot. Place the lamb rack, fat side down, in the pan, and brown well. Give each side a good sear, 5 to 10 minutes in total. Remove the skillet from the heat.
When the rack is cool enough to handle, transfer it to the prepared baking sheet. Brush the fat side of the rack generously with the mustard, and top with the breadcrumb mixture, packing it on lightly with your hands to form an even crust. Roast until an instant-read thermometer inserted in the center registers 135 degrees F (medium-rare), 25 to 30 minutes, or to your desired degree of doneness. Remove from the oven and let rest 15 minutes before carving between the bones.
To serve, smear some of the Apple-Mint Puree decoratively on 4 serving plates. Set two chops on the puree so their bones cross one another, and if desired, garnish with a mint sprig.
In a small bowl, combine all the ingredients thoroughly. Store in an airtight container for up to 6 months.
Peel and core the apples, chop them in 2-inch pieces, and add to a small pot. Add the cider, onion, and 2 teaspoons of the vinegar. Bring to a boil, reduce the heat to a simmer, and cook until the apples are tender and the flavors have come together, about 20 minutes. Remove from the heat.
Transfer the apple mixture to a blender and add the butter, mint, and remaining 1 teaspoon vinegar. Blend until you have a smooth puree. Serve warm. This will keep in an airtight container in the refrigerator for several days.
This recipe has been updated and may differ from what was originally published or broadcast.
Adapted from "Essential Emeril: Favorite Recipes and Hard-Won Wisdom from My Life in the Kitchen" by Emeril Lagasse © Oxmoor House 2015. Provided courtesy of Emeril Lagasse. All rights reserved.