Meanwhile, finely chop the remaining 1/4 cup of basil and set aside in a moist paper towel to keep fresh. In a medium stainless steel bowl, combine yolks and sugar, whisk for 2 to 3 minutes until it reaches a pale yellow color, and sugar is dissolved.
Reheat milk mixture until very hot but not boiling, and slowly pour about a third of it into eggs, whisking constantly. Then pour this mixture back into the saucepan with remaining milk. Over medium heat, stir constantly with a wooden spoon until thick and can coat the back of the spoon. Do not let it boil. Remove bean pods and strain seeds, beans and leaves while transferring into a large bowl. Allow the mixture to cool to room temperature, stirring occasionally.
Refrigerate for at least 2 hours. Using an ice cream machine, process according to manufacturer's instructions. Just before frozen, add reserved chopped basil to ice cream in the machine. Serve when firm enough to scoop.