Cut corn from cobs to equal 1 cup; cut cobs in half. In 4-quart saucepan, mix corn kernels, corn cobs, half-and-half and sugar. Heat to boiling over medium-high heat. Cover; remove from heat. Let stand 1 hour.
Discard corn cobs. In blender, place corn mixture. Cover; blend on medium-high speed about 1 minute or until smooth. Press mixture through strainer into large bowl. Stir in yogurt and basil.
Divide mixture evenly among ice pop molds. (If using paper cups, pour mixture into cups and cover with foil. With knife, make small slit in center of foil and slide craft stick through hole.) Freeze 8 hours or until firm. To serve, remove pops from molds or peel off paper cups.