1. Preheat grill to gill pan to moderate heat. Grill rolls, cut side down, until just golden, about 1 minute; set aside.
2. Combine mayonnaise, garlic, capers, and 1/4 teaspoon pepper in a small bowl. Cover and set aside.
3. Using hands, gently mix sirloin, onion, roasted pepper, bread crumbs, oil, bail, oregano, vinegar, rosemary, salt and remaining 1/4 teaspoon pepper in a medium bowl until just combined. Shape into 4 (1 inch thick) patties.
4. Lightly oil grill rack or pan. Grill burgers, turning once, about 8 minutes for medium well. Just before removing from grill, top each burger with 1 slice of cheese and heat until slightly melted.
5. Spread a heaping tablespoon mayonnaise mixture on bottom half of each bun. Layer with artichoke slices, burger and arugula; cover with top half of bun. Serve immediately.