Preheat the oven or toaster oven to 350ºF. Cut off and discard the top third of each head of garlic. Place the garlic heads cut side up on a small baking pan. Drizzle the cut sides with a little sunflower oil and roast until golden and tender, 20 to 30 minutes. Let cool.
Squeeze or peel the cloves from their husks. Place the roasted garlic in a blender or food processor. Add the beans, zest of 1/2 lemon, juice of the whole lemon, 1/4 teaspoon salt, the olive oil, and 1 tablespoon water. Blend until smooth, scraping down the sides of the blender as needed. Add more water as needed for your desired consistency. Season with salt to taste. Transfer to a serving bowl and chill at least 1 hour to meld the flavors.
To serve, top the dip with a swirl of olive oil and some freshly cracked pepper, and serve with crackers and sliced vegetables alongside.