1. Heat 1 teaspoon oil in a large nonstick skillet over medium heat. Add garlic; cook 1 minute or just until golden, stirring constantly. Add breadcrumbs; cook 1 minute or until lightly browned, stirring constantly. Transfer garlic mixture to a small bowl.
2. Separate leaves from Brussels sprouts; quarter cores. Heat remaining 1/2 teaspoon oil over medium heat. Add leaves and cores to pan; cook 8 minutes or just until leaves wilt and cores are crisp-tender, stirring frequently. Remove from heat; toss with breadcrumb mixture, salt, and pepper. Top with walnuts and cheese.