Preheat grill to 400℉.

Brush cut side of peaches halves with olive oil and then set aside.

Mix cinnamon and brown sugar in small bowl. Add butter and work into cinnamon sugar mixture with a fork until well incorporated.

Grill peaches starting with cut side down 2-3 minutes. Flip and grill about another 2 minutes. Remove from heat and place on a platter or serving dishes. Add a teaspoon of butter and cinnamon/sugar mixture to top of grilled peaches and spread around until it melts. Add a scoop of vanilla ice cream over peaches.

Heat butter mixture in microwave-safe bowl for 15 seconds. Add a drizzle of melted butter mixture to top of ice cream and serve immediately.