1. Combine 1 1/2 cups water and chiles in a microwave-safe bowl; microwave at HIGH 2 minutes. Let stand 15 minutes. Remove chiles; discard liquid. Stem and seed chiles. Combine chiles, 1 teaspoon oil, and garlic in a mini food processor; process until smooth. Combine chile mixture, sugar, and next 4 ingredients (through beef) in a medium bowl. Stir in 1/4 teaspoon salt. Divide beef mixture into 4 equal portions. Gently shape each into a 1/2-inch-thick patty.
2. Using a knife, remove needles from nopales; peel nopales, and chop to measure 1 cup. Heat a medium skillet over medium-high heat. Add the remaining 2 teaspoons oil; swirl to coat. Add nopales; sauté 3 minutes or until tender.
3. Preheat grill to medium-high heat.
4. Combine nopales, jicama, cilantro, and juice in a small bowl; sprinkle with remaining 1/8 teaspoon salt.
5. Place patties on grill rack coated with cooking spray; grill 3 minutes. Carefully turn patties; grill 3 minutes or until desired degree of doneness. Place 1 patty on bottom half of each bun; top each serving with 1/4 cup jicama mixture and top half of bun.