Set your pellet grill or smoker to 375°F.
Slice off the bottom of the pineapple, leaving a flat surface.
While leaving the crown on the pineapple, slice off the shell using a sharp knife and slice from the crown down to the bottom, removing any part of the shell.
Mix 2 tablespoons of melted butter in a small bowl with about 5 heaping tablespoons of brown sugar. Mix well until combined into a thick paste. Add more brown sugar if needed.
Using your fingers, spread the brown sugar paste over the pineapple's yellow flesh, making sure to coat the entire surface on all sides.
Place the pineapple in the center of the lowest rack and close the lid.
Turn or rotate the pineapple slightly every 5 minutes, so a new sliced surface is exposed to the grill grates.
Continue rotating the pineapple until all the sides are cooked to your preference. This should take approximately 30 minutes.
Once the pineapple has dark grill marks on all sides and is cooked to your liking, remove it.
Immediately slice in the same direction you followed when removing the shell. Slice around the entire pineapple once or twice until you've removed all the fruit down to the core.
Sprinkle the slices with a coarse sea salt or kosher salt.
Serve warm!