Add the butter to a medium saucepan set over medium heat and cook until melted.
Stir in the sugar, salt and heavy cream until it’s well-combined then bring the mixture to a boil, scraping down the sides with a rubber spatula as needed, and boil it for 4 to 5 minutes.
Remove the caramel from the heat and stir in the vanilla extract and bourbon. Set the sauce aside to cool slightly. (It will thicken as it cools.)
Oil the grill then halve the peaches and remove the pits. Arrange the peaches on the grill, cut side down, and grill until warm and caramelized.
Transfer the peaches to serving plates, top each with a scoop of ice cream and drizzle with caramel sauce. Serve immediately.
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