Preheat oven to 400 F.

Remove most of the papery covering from garlic, leaving just enough to keep the bulb intact. Cut bottom off bulb to remove the root and expose the cloves. In small casserole dish with lid (such as a brie baker), place shallot and garlic, drizzle with olive oil, and add thyme sprig. Cover and bake for 45 minutes, or until garlic is soft and beginning to brown. Remove lid and allow to cool. Discard thyme sprig.

In bowl of food processor, place drained, unrinsed beans. Using toothpick or small fork, skewer each garlic clove to remove flesh and add to food processor, along with entire shallot and roasting oil, vinegar, salt, and pepper. Blend until smooth and creamy. Stir in half of the thyme leaves and transfer mixture to serving bowl. Sprinkle remaining thyme leaves on top.