Preheat a gas grill to medium-high heat, or prepare a medium-hot fire in a charcoal grill.
In a small saucepan, whisk together the brown sugar, tequila and 1/4 cup water. Set the pan on the grill (or a side burner on medium-high heat) and cook, stirring, until the sugar is dissolved and the mixture comes to a boil. Remove from the heat and let stand until cool.
Put the pineapple slices in a baking dish and pour the cooled syrup over them, tossing gently to coat. Let stand at least 5 minutes and up to 30 minutes.
Whip the heavy cream in a bowl to the soft-peak stage. Refrigerate until ready to use.
Spread the butter on both sides of each pound cake slice and grill, turning once, until light golden, about 1 minute per side. Drain the pineapple, reserving the syrup, and grill, turning once, until grill marks appear, about 1 minute per side.
To assemble, place each pound cake slice on a dessert plate and top with 2 pineapple rings. Drizzle a little of the tequila syrup over each plate, top with a dollop of whipped cream and garnish with a mint sprig and some chopped mint.