Preheat oven to 400°F. Toss tomatoes with a drizzle of olive oil, garlic, salt, pepper and thyme; sprinkle with a drizzle of vinegar. Roast until tomatoes are slumped, about 30 minutes; remove.
In a deep-sided skillet, bring a few inches of water to a boil. Salt water and boil broccoli rabe for 4-5 minutes; cold shock and drain well. Chop about 1 (packed) cup greens and reserve the rest for another use (like a frittata).