Heat the olive oil in a pot over medium heat. Add 6 garlic cloves and sauté until golden, 2 minutes. Add the broccoli rabe, red pepper flakes and a pinch of salt. Cover and cook, tossing occasionally, until tender, 8 to 12 minutes.
Meanwhile, grill the bread on a grill pan over medium heat until well marked and golden, 2 to 3 minutes per side. Rub both sides with the remaining smashed garlic clove and brush with olive oil; season with salt and pepper.
Serve the broccoli rabe with burrata, flaky sea salt and the grilled garlic bread.