Preheat the oven to 375°F. Line a baking sheet or shallow dish with parchment paper. Cut the squash in half and remove the seeds. Brush a little oil on the surface of the squash and sprinkle with salt. Place, flesh-side down, on the prepared sheet and roast for about 40 minutes, or until tender. Cool the squash until you can handle it safely, then scoop the flesh from the skin. You should have about 3 cups of packed, roasted squash.
In a large Dutch oven or heavy soup pot, heat 2 tablespoons vegetable oil over medium heat. Add the diced onion and a large pinch of salt. Cook until the onion softens (don't let it brown), then add the garlic and ginger. Stir and cook for another 2 to 3 minutes until everything is fragrant. Add the roasted squash, chopped kimchi, 3 cups of the stock (reserve the remainder to adjust the consistency of the soup later), another big pinch of salt, and the coconut milk to the pot. Bring up to a simmer, partially cover, and cook for 20 minutes.
Turn the heat off under the pot and let the soup cool for a few minutes. Puree the soup, with an immersion blender or in batches in a regular blender, until smooth. Strain through a fine-mesh sieve into a clean pot. If you wish to adjust the thickness of the soup add some of the reserved chicken stock. I like soup to be "soupy" so I added the entire reserved cup of stock. Now check for seasoning: squeeze in some lime juice, add more salt and some pepper, to taste. Swirl in a couple of tablespoons of cream and taste again. You should have a balance of sweet, salty, spicy, and creamy. Add the remaining cream, if you like, and additional salt, pepper, and lime juice to taste. Keep the soup warm while you prepare the garnish.
Melt the butter in a small skillet. Add the chili oil, if using. Add the pumpkin seeds and toast, over medium-high heat, until golden and crunchy. Portion the soup into bowls and spoon some buttery, spicy pumpkin seeds atop each serving. Store any leftovers in an airtight container in the refrigerator for 2 to 3 days.