Preheat grill or grill pan to medium-high heat.
Place banana slices on the grill and cook for 3-4 minutes per side, or until lightly charred and softened.
Remove bananas from the heat and set aside.
In a small saucepan, combine brown sugar, heavy cream, butter, and vanilla extract.
Heat the mixture over medium heat, stirring constantly, until the sugar is dissolved and the mixture is thick and bubbly.
Pour the caramel sauce over the grilled banana slices and serve immediately.