Prepare the Lamb: Preheat oven to 375°F. Let lamb stand at room temperature 15 minutes. Sprinkle with 3/4 teaspoon each salt and black pepper. Heat oil in a large heavy-duty ovenproof skillet over high. When the oil is very hot, add lamb, and cook until browned, 3 to 5 minutes per side. Transfer to a cutting board, meat side up.
Stir together mustard, crushed red pepper, and finely chopped garlic in a small bowl. Place pecans in a large shallow dish.
Brush mustard mixture across the top of the rack until coated. Carefully dredge rack in pecans to coat evenly. Return lamb to skillet, pecan side up, and transfer to preheated oven. Bake until a thermometer inserted in thickest portion registers 145°F, 15 to 18 minutes. Increase heat to broil, and broil until pecans are lightly browned, about 2 minutes.
Meanwhile, prepare the Sauce: Stir together yogurt, mint, cilantro, and pressed garlic in a small bowl. Stir in 1/4 teaspoon each salt and black pepper.
Remove lamb from oven, and transfer lamb to a carving board, preferably with a moat. Cover with aluminum foil, and let rest about 5 minutes before slicing. Slice between the bones, forming either single or double chops. Place on a warmed serving platter, and garnish with mint and cilantro, if desired. Serve immediately with Mint Dipping Sauce.