Place oven rack in the lower half of the oven and preheat oven to 425 (220C) degrees.
Use a large heavy knife to slice off the stem and bottom ends of the squash. Slice squash in half and scoop out the seeds with a spoon. Slice the squash into 1-inch wide slices. Cut them in half if they're larger than 4-inches wide.
Toss the slices with the olive oil, 1 1/2 teaspoons salt and chili flakes. Arrange cut-side down on a large rimmed baking sheet without crowding (use 2 sheets if you need to).
Roast 25 minutes, or until the squash is tender (test with the tip of a knife) and golden brown on the edges. Remove from the oven and immediately sprinkle the cheese over the squash.
Heat a small skillet over medium heat. Add the butter and let it melt and bubble, swirling the pan. When the butter begins to foam, turn up the heat to medium-high and cook until the butter turns amber and smells nutty — this should take just a few minutes. Remove the butter from the heat and stir in the honey.
Transfer the squash to a serving platter, using a spatula to grab all the cheesy bits. Top with the parsley and green onions. Pour the hot honey butter over the squash and serve.
Leftover squash keeps well for 3-5 days. Keep refrigerated in covered container.
Reheat in a microwave, or in a 350 degree oven for 15 minutes.