Heat oven to 450°F. Heat large cast-iron skillet on medium-high. Season steaks with salt and pepper. Add 1 teaspoon oil to skillet, then add steaks and garlic and cook until steaks are browned, 3 minutes per side.

Place tomatoes on the vine and rosemary in skillet, drizzle with 2 teaspoons oil and season with salt and pepper. Transfer skillet to oven and roast until steak is at desired doneness and tomatoes begin to slightly break down, 3 to 4 minutes for medium-rare. Transfer steaks to cutting board and let rest at least 5 minutes before serving. Transfer tomatoes and garlic to platter; squeeze garlic cloves from skins.

In small bowl, combine vinegar, remaining 3 tablespoons oil, and 1/4 teaspoon each salt and pepper; stir in onion and fold in blue cheese. Serve steak, tomatoes, and garlic drizzled with vinaigrette, and arugula salad.