Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Combine the paste ingredients. Coat the lamb with the paste, adding more on the meaty side than the bone side. Cover and refrigerate for 1 to 2 hours.
Cut off and discard the top third of the garlic head to expose the cloves, and then place on top of a 6-inch square of aluminum foil. Drizzle the exposed cloves with oil. Fold up the corners of the foil to seal the packet.
Brush the cooking grates clean. Grill the garlic packet over indirect medium heat, with the lid closed, until soft and golden, about 40 minutes. Remove from the grill, open the packet, and let cool for 10 minutes. Squeeze the garlic cloves from their papery shells into a small bowl and mash any large pieces.
Allow the lamb to stand at room temperature for 15 to 30 minutes before grilling. Sear the lamb, bone side down first, over direct medium heat, with the lid closed, for 3 to 5 minutes, turning once and watching closely to avoid flare-ups. Move over indirect medium heat, and cook, meat side down, with the lid closed, to your desired doneness, 15 to 20 minutes for medium rare, turning once. Meanwhile, prepare the beans.
In a medium saucepan over medium heat, warm 2 tablespoons oil. Add the shallots and cook until softened, about 4 minutes, stirring occasionally. Add 1½ tablespoons of the roasted garlic, the red pepper flakes, rosemary, and black pepper and cook until fragrant, about 1 minute, stirring constantly. Add the beans and stir to coat. Add the water and tomato paste, bring to a simmer, and cook, covered, over low heat, for about 10 minutes, stirring occasionally. Add more water, if necessary. Season with salt and transfer to a serving bowl. Stir in the parsley and drizzle with oil.
Remove the lamb from the grill and let rest for about 10 minutes. Cut the lamb between the bones into individual chops and serve warm with the beans.