Add basil to a food processor and process a few seconds to break up the leaves.
Mince garlic; drain and rinse beans. Add both to the food processor along with juice from the lemon, tahini, and salt; process 1 minute or until pureed.
Add olive oil to the food processor 1 tablespoon at a time through the feed chute.
Add water 1 tablespoon at a time until the desired consistency is reached.
Serve immediately with veggies on the side for dipping.