Roast the chiles over an open flame or close up under a preheated broiler, turning regularly until the skin is blackened and blistered all over, about 4 minutes for an open flame, 6 minutes for a broiler. Cool, then pull off the stems, slice the chiles in half lengthwise, gently scrape out the seeds, then flip the chiles over and scrape off the charred skin. Slice the cleaned chile pieces crosswise into ¼-inch strips.
Lightly salt the squash. In a heavy, dry, large (10-inch) skillet over medium-high heat (or on a grill pan or prepared charcoal or heated gas grill), dry-roast (or dry-grill) the summer squash in a single layer, turning frequently, until lightly charred on all sides but still a little crunchy, about 12 minutes.
When you’re ready to serve, combine the summer squash, chiles and ¼ cup of the garlic mixture in the skillet over medium heat. Stir until hot, then taste and season with salt (usually about ¼ teaspoon). Scrape into a warm serving bowl, then sprinkle with cilantro and cheese. You’re ready to serve.