Transfer garlic and oil to a blender. Add vinegar, granulated sugar, salt, and pepper and blend until very smooth. Pour into a jar and refrigerate until ready to use.
03<strong>Make Ahead: </strong>Dressing can be made 1 week ahead. Keep refrigerated.
04Salad: Prepare a grill for medium-high heat; preheat 5 minutes and clean grates. Drizzle onion with oil; season with salt. Generously season steak with salt and pepper.
05Grill onions, turning once, until char marks appear, 2 to 3 minutes per side, and grill steak, turning occasionally, until an instant-read thermometer inserted into thickest part registers 130° for medium-rare, about 6 minutes per side. Transfer onions and steak to a cutting board. Let cool slightly. Thinly slice steak against the grain.
06On a large platter, arrange arugula. Top with steak, onions, avocado, tomatoes, blue cheese, and basil. Drizzle with dressing before serving.