In a blender, combine all ingredients except for the chopped dark chocolate. Blend on medium to high, until everything is combined. Pour matcha mixture into popsicle molds, taking care NOT to fill them up completely, only 3/4 of the way full to leave room for the chopped chocolate. Distribute the chocolate evenly between the popsicles, dropping in the pieces and letting them sink to the bottom. Freeze for at least 4 hours, or until firm.