Place the sage on a paper towel and leave it in a cool dry place to dry it out for 8 hours or up to overnight.
Heat a smoker to 350 degrees F with char-hickory pellets.
Cut the neck or narrow end of the butternut squash off to separate it from the round, bulbous bottom end. Scoop the seeds out of the squash bottom and reserve to use as a dip bowl. Peel the narrow end and cut into about 1-inch dice. (You should have about 4 cups of diced squash.)
Melt the butter in a medium saucepan over medium-high heat. Add the squash, chipotle chile and some salt and saute until the squash starts to caramelize, about 10 minutes. Meanwhile, toss the shredded cheeses with the cornstarch in a bowl and set aside. Add 1 cup water to the squash, then simmer until very tender, about another 10 minutes. Add the milk, then blend using an immersion blender until silky and smooth. Add the cheese, then stir well to help melt the cheese. Season to taste with salt. Transfer the pan to the smoker and let the queso absorb that wonderful smoke until the color is darker and the flavor is smokier, about 30 minutes.
Draw a face on your squash bottom if you wish, then add the dip directly to the squash. Carefully light the dried-out sage, then blow it out to create smoke and stick it straight up in your dip. Cover it with a dome or deep bowl (tall enough not to smush the sage bunch); this will infuse the flavor and keep the demons and ghouls away. Remove the dome right when guests are ready to eat. Serve with kale chips, tortilla chips, raw veggies or soft pretzels.