How to Make It
Cook pasta in a large pot of boiling salted water until al dente, 8 to 10 minutes; drain.
Meanwhile, heat a grill pan over medium-high. Toss tomatoes, oregano, 1 tablespoon of the oil, ½ teaspoon of the salt, and ¼ teaspoon of the pepper in a large bowl. (Do not clean bowl.) Place tomatoes in a single layer on hot grill pan, and grill, flipping once, until well marked and soft, 4 to 5 minutes per side. Combine grilled tomatoes, vinegar, ¼ cup of the oil, ½ teaspoon of the salt, and ¼ teaspoon of the pepper in a blender and process until smooth.
Place onion and broccoli rabe in bowl. Add remaining 3 tablespoons oil, ½ teaspoon salt, and ¼ teaspoon pepper and toss to coat. Place onion slices in a single layer on hot grill pan, and grill until well marked and tender, 4 to 5 minutes per side. Remove from pan. Place broccoli rabe in hot grill pan, and grill until tender-crisp, 2 to 3 minutes per side. Coarsely chop vegetables and return to bowl. Add pasta, tomato vinaigrette, and mozzarella and toss to combine.