Preheat the oven to 400°F. Slice about 1/4 inch off the top of the garlic head to expose the cloves, place it on a small piece of foil, drizzle with 1 tablespoon olive oil, wrap loosely, and set it on a small baking dish or directly on the oven rack.
Roast the garlic for 35 to 40 minutes, until the cloves are very soft and lightly golden. Remove it from the oven and let it cool for about 10 minutes, until comfortable to handle.
Squeeze the roasted garlic cloves into the bowl of a food processor, discarding the papery skins. Add the drained and rinsed cannellini beans, 3 tablespoons extra-virgin olive oil, lemon juice, lemon zest, kosher salt, and black pepper.
Process the mixture until mostly smooth, then add 2 tablespoons water and continue blending. Stop and scrape down the sides as needed so the dip blends evenly.
Blend again until the dip is creamy and smooth. If it seems too thick, add the remaining water 1 tablespoon at a time until it reaches your preferred consistency.
Taste the dip and adjust if needed with a little more salt or lemon juice. Spoon it into a serving bowl and use the back of a spoon to create a shallow swirl on top.
Drizzle the top with 1 teaspoon extra-virgin olive oil and sprinkle with chopped parsley. Serve right away with crackers, toasted pita, or fresh vegetables, or chill until ready to serve.