We took a perennial favorite--sweet potato pie--and mashed it together with a twice-baked potato to make an outrageously decadent side dish. The heat from the grill makes the marshmallows puff and turn golden, while the smokiness balances the sweetness.
Prepare a grill for medium-high indirect heat: For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes, turn off one of the middle burners and leave the remaining burners at medium high. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. Replenish the charcoal as needed. (Be sure to consult the grill manufacturer's guide for best results.)
Grill the sweet potatoes until cooked through but still holding their shape, about 50 minutes. Let cool until they can be handled, about 15 minutes.
Meanwhile, put the butter in a small skillet over medium-high heat and cook, swirling often, until it melts and turns golden brown, about 4 minutes.
Cut the potatoes in half and scoop the flesh into a large bowl; keep the skins intact. Add the brown butter, cream, sugar, vanilla and 1/2 teaspoon salt to the flesh and mash with a potato masher until smooth.
Put the potato skins in a grill basket, spoon the filling back into the skins and top each with 2 marshmallows. Do not put the basket lid back on the grill basket. Put the grill basket on the grill, cover the grill and cook until the filling is hot and bubbling around the edges and the marshmallows are golden, about 10 minutes. Let cool about 5 minutes before serving.
To save time, you can cook the whole potatoes in the microwave first, then finish the stuffed skins on the grill (but the skins won't be as smoky or crisp).