In a small bowl, combine sugar and cinnamon; sprinkle over cut sides of peach. Let stand for 5 minutes.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Place peach cut side down on grill rack. Grill, covered, over medium heat for 8-10 minutes or until peach is tender and begins to caramelize.
Place peach halves in dessert bowls. Serve with ice cream and granola.
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