1. Place honey in a medium saucepan over medium heat; cook 2 minutes or until heated. Add onions to pan; stir to combine. Stir in vinegar; bring to a boil. Cover, reduce heat, and simmer 30 minutes or until onions are tender. Cook, uncovered, 20 minutes or until syrupy.
2. Preheat oven to 375°.
3. Heat an ovenproof grill pan over medium-high heat. Add 1 tablespoon oil to pan, swirling to coat. Sprinkle endive evenly with 1/4 teaspoon salt and 1/4 teaspoon black pepper. Add endive, cut sides down, to pan. Cook 1 minute or until lightly browned. Turn endive; place pan in oven. Bake at 375° for 15 minutes or until endive is tender. Remove endive from oven; cover and keep warm. Wipe pan clean.
4. Combine remaining 1/2 teaspoon salt, remaining 1/2 teaspoon pepper, 1 tablespoon oregano, and paprika in a small bowl. Sprinkle beef evenly with oregano mixture. Heat grill pan over medium-high heat. Add remaining 1 tablespoon oil to pan, swirling to coat. Add beef to pan; cook 4 minutes on each side or until desired degree of doneness. Let stand 10 minutes before cutting across the grain into thin slices.
5. Combine remaining 1 tablespoon oregano, arugula, oil, and juice in a medium bowl; toss gently. Serve steak with endive and arugula salad; top steak with onion mixture.