Preheat the oven to 385 degrees F
Trim the ends from the squash and cut in half. Discard the seeds.
Peel the squash and cut into small dice about 1-inch square.
Transfer the diced squash to a bowl and add the olive oil. Toss well coating all of the squash.
Place the squash onto a large baking tray and add the chopped bacon and 1 tbsp of the chopped thyme. Mix together.
Season with salt and pepper and bake in the oven for 45 minutes and the squash can be pierced easily with a knife. About halfway through cooking move the squash around to promote even cooking.
Combine the diced jalapeno and 1/4 cup olive oil and set aside.
In a pan over medium heat, cook the diced onion until soft.
Add the garlic, tarragon, nutmeg and remaining 1 tbsp of chopped thyme and cook for 2 minutes.
Transfer all of the squash including bacon and bacon fat from the tray to a blender or food processor and add the onion mixture.
Add 3 cups of chicken broth and blend on high power.
Using a wooden spoon, move the squash around the blender and add 1 more cup of broth.
Blend on high until smooth and lump free.
Transfer the mixture to a 2-quart pot and bring to a simmer.
Add the cream and stir.
Add more broth if you prefer the soup to be thinner at this part.
Pass the chili oil through a small sieve and discard the diced chili.
Serve the soup in bowls and garnish with some chopped pistachios and a drizzle of the chili oil on top.