Cut peaches along seam all the way around and twist halves off the pit.
Brush peaches with oil and cook, cut side down until fruit has grill marks, 3 to 4 minutes.
Caramel Sauce:
Mix brown sugar, half-and-half, butter and salt in saucepan over medium-low heat. Cook while whisking gently for 5 to 7 minutes, until thick. Add vanilla and cook another minute.
Notes
Serve your yummy grilled peaches with vanilla ice cream drizzled with caramel sauce! #nomnomnom