Preheat oven to 375 degrees F. Line large roasting pan with foil; set aside. In bowl toss onion with 1 tablespoon of the oil, 1/4 teaspoon of the salt, and 1/4 teaspoon of the pepper; set aside.
Heat 1 tablespoon of the oil in large skillet; add onion mixture. Cook over medium-high heat 5 minutes, stirring occasionally, until onions begin to brown. Reduce heat to medium-low. Add broth and vinegar. Cover; cook 15 minutes or until onions are tender. Add butter. Increase heat to high. Cook 2 to 3 minutes, shaking pan occasionally, until onions are glazed.
Meanwhile, add kale to roasting pan. Toss with remaining oil, garlic, salt, and pepper. Roast, uncovered, 15 minutes, tossing 3 times. To serve, gently toss with onions. Serves 8.