Roast the garlic: Heat the oven to 400 degrees. Peel off most of the garlic's outermost skin but leave the whole head intact. Trim about ¼ inch off the top of the garlic to expose the cloves. Place the garlic on a large piece of aluminum foil, then drizzle 1 teaspoon olive oil over the exposed cloves and close the foil into a pouch. Bake for 40 to 50 minutes, until you can pierce the center of the head with a knife. Let cool slightly.

Squeeze the roasted garlic cloves into the bowl of a food processor. Add the white beans, 4 tablespoons olive oil, lemon juice, rosemary leaves, black pepper, cayenne (if using), hot water and salt. Purée until smooth, then taste for salt, pepper, rosemary and lemon juice. Adjust as necessary. Transfer to a serving dish.

Heat remaining 1 tablespoon of olive oil in a small heavy skillet over medium-high heat. When hot, add the remaining rosemary sprig — it should sizzle. Cook until brown and crisp, flipping once, about 1 minute per side, then transfer to the top of the dip as a garnish. Pour or spoon the remaining olive oil, now infused with rosemary, over the top of the dip. Sprinkle with cayenne for a little additional heat.