Preheat oven to 350ºF. Place the garlic and 1 tablespoon of olive oil in some tin foil and make a pouch with it. Place this foil pouch in the oven and roast for about 30 minutes or until the garlic cloves are soft and slightly browned.
Drain and rinse the beans and put them in the bowl of a food processor. Add in the tahini, roasted garlic, and barbecue sauce. Pulse a few times to chop up the beans.
Remove the lid, scrape the sides down with a spoon or rubber spatula, and turn the machine back on. While the motor is running, drizzle in the 1/4 cup of olive oil. Remove the lid and scrape down the sides again.
Add in some fresh lemon juice and a large pinch each of salt and pepper. Blend again and season with more lemon juice, salt, pepper, or barbecue sauce to taste.
Serve immediately, drizzled with a little olive oil or place in a resealable container and refrigerate until ready for use. Keep in the refrigerator for up to one week.
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