Heat the oven to 400°F. Slice a thin piece off both ends of the squash, including the stem. Cut the squash in half crosswise (perpendicular to the ribs). Scoop out the seeds with a sturdy spoon.
Grip the squash at one end and use swift, deliberate, forceful strokes to cut the tip off the opposite end.
Trim just enough to remove the stem about 3/4 inch); any more and you’ll create a hole in the bottom of the “cup.”
After cutting the trimmed squash in half, remove the seeds and any extra fibers with a sturdy spoon.
Line a rimmed baking sheet, jellyroll pan, or shallow baking dish with foil or parchment. (If you’re only cooking two halves, be sure to use a small pan that the squash will fit into somewhat snugly.) If you use foil, rub it with butter to keep the squash from sticking.
Set the squash halves on the prepared baking sheet and smear the flesh all over with the softened butter (for the Parmesan Thyme Squash, just drizzle the olive oil all over). Sprinkle with the salt. Sprinkle or drizzle the remaining ingredients over the top edge of the squash and into the cavity (most of the liquid will pool up there).
Roast the squash halves until nicely browned and very tender (poke in several places with a fork to test), about 1 hour and 15 min. for small to medium squash; larger squash may take longer. Don’t undercook. Serve warm with a spoon.