COOK IT.
Place your sweet potatoes over indirect heat, and grill for about 50 minutes. You want them cooked through, while still holding their shape. Use a fork or knife to check for tenderness.
Pull your potatoes off the grill and allow them to cool until you can handle them safely (about 15 minutes).
Put 4 tbsp of unsalted butter in a small skillet over medium-high heat for about 4 minutes. Stir and swirl the butter often until it’s fully melted and has turned golden brown.
Cut the potatoes in half lengthwise. Then take a spoon and scoop out the interior into a large bowl, being careful to keep the potato skins intact.
Add your brown butter, ¼ c heavy cream, ¼ c packed light brown sugar, 1 tsp pure vanilla extract, and pinch of kosher salt in with the removed sweet potato, and mash with a fork or potato masher until smooth.
Line up the empty potato skins on an open grill basket or a mesh grill tray. Then spoon the filling back into the skins, and top with medium/large marshmallows.
Place your grill basket (open, not closed) or tray back on the grill over indirect heat, cover, and cook for about 10 minutes until the filling is hot and bubbling around the edges and the marshmallows appear golden.
Let your stuffed potatoes cool for about 5 minutes, and serve.