To cook the kabocha squash in the oven, you will need to cut the squash in fourths. The skin is very tough. To soften it, microwave the squash for 4 minutes. Use a very sharp chef’s knife or cleaver and a rocking motion to carefully cut into the squash on the grooves.
Preheat the oven to 400°F (205°C).
Scoop out the seeds and stringy bits. Place the squash, flesh side up, on a baking sheet lined with parchment paper or a silicon mat. Rub 1 tablespoon olive oil over all sides, and sprinkle with salt. Turn them skin side up. Roast for 45-55 minutes, until the squash is soft.
To cook the squash in an Instant Pot, there is no need to cut the squash. Place it whole on the trivet in the Instant Pot. Pour in 1 cup of water.
Secure the lid and set the vent to sealing (if necessary for your model).
Set to cook on high pressure for 20 minutes. When done, allow the pressure to release naturally.
Carefully pull the trivet with the squash on it out of the Instant Pot. Allow it to cool for 10 minutes. Peel back the skin, cut in half, and scoop out the seeds.
In a large pot over medium heat, add the oil and when hot, add the onion and saute for 5 minutes. Add the garlic, rosemary and salt. Stir to combine.
Add the squash and vegetable stock to the pot. Cover and cook for 10 minutes over low heat.
Puree the soup with an immersion blender until silky smooth, about 3 minutes.
Garnish with fresh herbs, if desired.