Place the peaches, cut side down over high heat and let cook until you see those nice grill marks (5-7 minutes depending on your grill).
Place the peaches, cut side up on a small sheet pan or other heat proof pan.
Sprinkle about 1 tbl of brown sugar over each half and put the sheet pan back on the grill over medium/low heat, close the lid and cook about 10 minutes - the time depends on how ripe your peaches are, if they are super tender and juicy they might only need enough time to melt the sugar, if they need a little tlc, cook them until a knife pierces them easily.
Serve warm or room temp plain, with a scoop of ice cream, a dollop of whipped cream, anything and everything.
Recipe by Eat Some Wear Some at https://eatsomewearsome.com/grilled-peaches/