Set a large (10-inch) skillet (nonstick or lined with foil) over medium-high heat and lay in the garlic and tomatillos (cut side down). When the tomatillos are well browned and soft, 5 to 6 minutes, flip everything over and brown the other side. (The garlic should be soft.) Cool, then peel the garlic.
In a blender, combine the garlic, tomatillos, chipotles and 1 cup water. Blend to a coarse puree.
Scoop the butternut pieces into a microwave-safe bowl, cover with plastic wrap, poke a few holes in the top and microwave on high for 4 minutes. Meanwhile, in a large (10-inch) skillet set over medium, cook the bacon, stirring occasionally, until crispy, 5 to 7 minutes. Add the butternut and tomatillo sauce to the pan, raise the heat to medium-high and bring the sauce to a brisk simmer. Cook until the butternut is fork-tender and the sauce has reduced by about half its volume, about 15 minutes. Taste and season with salt (it will need only about ¼ teaspoon because of the bacon’s saltiness). Scrape into a serving bowl and finish with a generous sprinkling of the queso.