Slice off the very top of the garlic head. Drizzle the head with olive oil and wrap in foil. Place on a sheet tray and bake until tender and fragrant, roughly 35 minutes. Remove from the oven and let cool. Remove the cloves and mash with a wooden spoon.
Add the olive oil, basil, mint, beans, lemon juice, and some salt and pepper to a food processor and pulse until smooth. For a smooth texture, leave the machine running for a moment. Serve with the vegetables and baked tortilla chips.
Make this dip a few hours ahead of time so the flavors have time to marry.