Place chicken skin flat on a jelly-roll pan lined with parchment paper. Bake at 375° for 40 minutes, making sure skin gets brown and thoroughly crisp but not burned. Drain on paper towels. Chop skin into small pieces; toss with 1/4 teaspoon salt in a bowl. Set aside.
Combine 2/3 cup vinegar, 3/4 cup sugar, and 1/2 cup water in a saucepan; bring to a boil. Remove from heat; add carrots and broccoli. Let stand 30 minutes. Drain.
Combine cilantro, parsley, pepper, 1/2 teaspoon sugar, and garlic in a mini food processor; process until finely chopped. Add remaining 1/3 cup vinegar and oil; pulse until well combined. Combine 1/2 cup sauce and beef in a large zip-top plastic bag; turn to coat. Let stand at room temperature 30 minutes, turning once.
Heat a large grill pan over medium-high heat. Coat pan with cooking spray. Add steak to pan; cook 5 minutes on each side or until desired degree of doneness. Remove steak from pan; let stand for 5 minutes. Cut steak across the grain into thin slices; sprinkle with remaining 1/4 teaspoon salt.
Heat tortillas according to directions. Divide steak, vegetables, and remaining 1/3 cup sauce among tacos. Sprinkle each taco with about 2 teaspoons chicken skin; serve with lime wedges.