1. Preheat oven to 400 degrees. Drizzle 6 tablespoons oil on a rimmed baking sheet. Season with salt and pepper. Add whole garlic, thyme, and tomatoes, cut sides down. Bake until tomato skins blister, about 25 minutes. Remove from oven; peel off tomato skins. Lower oven to 325 degrees. Return tomatoes to oven; bake for 30 minutes. Let cool on pan. Discard garlic and thyme.

2. Bring a large pot of salted water to a boil. Prepare an ice-water bath. Add broccoli rabe in 2 batches to boiling water; blanch for 20 seconds. Transfer to ice water. Drain and chop roughly.

3. Heat 4 tablespoons oil in a large saute pan over medium heat. Add sliced garlic; saute until lightly golden, about 4 minutes. Add broccoli rabe and stock. Stir in red pepper flakes. Season with salt. Add tomatoes and their juices and cook over medium heat, simmering until broccoli is tender. Season again.