For the Lamb Chops, mix sugar, cardamom, cumin, cinnamon and ginger in small bowl. Brush lamb chops with oil. Coat with garlic, then spice mixture. Refrigerate at least 2 hours or overnight.
For the Vanilla Sauce, melt 2 tablespoons of the butter in large skillet on medium heat. Add mushrooms; cook and stir 5 to 7 minutes or until golden brown. Remove from skillet. Melt remaining 1 tablespoon butter in same skillet on medium heat. Add shallots; cook and stir 2 minutes or until softened. Stir in balsamic vinegar and chicken broth. Bring to boil. Reduce heat to low; simmer 15 minutes or until sauce is reduced by half and slightly thickened. Stir in cream, vanilla and mushrooms. Simmer until heated through.
Meanwhile, season lamb chops with sea salt and pepper. Grill over medium-high heat 8 to 10 minutes or until desired doneness, turning once. Serve lamb chops with Vanilla Sauce.