Peel the squash or pumpkin, chop off the stem end and cut it in half lengthwise, slicing through the cavity that holds the seeds. Wrap and refrigerate half for another use; from the other half, scoop out the seeds and pull off the stringy fibers that entangle them (if a few remain, that’s okay). Scoop the seeds into a small bowl (you should have about ¼ cup) and chop the squash or pumpkin into roughly 1-inch pieces (you should have about 3 cups).
Melt the butter in a medium (3-quart) saucepan set over medium heat. Add the seeds and onion, and cook, stirring frequently, until the onions are richly golden and the seeds have started to brown, about 10 minutes. Add the chile pieces and cook, stirring, for a minute or two, until they are fragrant and lightly toasted. Add the squash (or pumpkin), apple, pepper, cinnamon and 1 quart water. Bring to a boil, then reduce the heat and let the mixture simmer until everything is very tender, about 30 minutes. Ladle into a blender, loosely cover and blend until completely smooth. (A large, high-powered blender like Vitamix works best here; if yours is smaller, blend in batches. An immersion blender, while easy, will barely blend the seeds.) Set a medium-mesh strainer over the pot and pass the soup through. Season with salt (usually about 1 teaspoon) and a little sugar (½ teaspoon or so brings out the flavor of the apple). Serve warm in warm bowls.