Combine the sliced peaches and sugar in a food processor; pulse until finely chopped. Add the cottage cheese and process until almost smooth. Add the sweetened condensed milk; pulse until combined.
Freeze in a 2-quart ice cream maker according to the manufacturer’s directions (20 to 30 minutes). Place in a covered container and freeze for 4 to 6 hours or until easy to scoop.
If frozen for an extended period, let stand at room temperature to soften slightly. Meanwhile, heat the grill. Brush the quartered fresh peaches with the oil.
Grill the peaches over medium to medium-low heat for 2 to 4 minutes or until slightly softened. Slice and serve with the ice cream.