Preheat oven to 450. Cut cauliflower into florets of equal size. Toss with olive oil, sprinkle with salt and pepper, spread out on a baking sheet. Roast until nicely browned - check at about 20 minutes. Mine took about 40 minutes but my oven runs cool.
Peel shallots, cut in half lengthwise, and slice. In a soup pot, heat coconut oil. Add shallots, cook on medium heat and stir regularly until soft and taking on some color.
While shallots are cooking, peel and dice the turmeric. Seed and dice the hot pepper. (Then wash your hands!) Add turmeric and hot pepper to the pot, stir and cook for 1-2 more minutes.
Add roasted cauliflower to the pot. Add the coconut milk and vegetable or chicken stock. Bring to a boil, then lower to a simmer and cook for a couple more minutes.
Remove from heat. Add juice of the lime, the ground turmeric, and a drizzle of chili oil. Blend with an immersion blender or in a blender. Taste for seasoning, add salt and pepper to taste. If in blender, return to pot and warm.
To serve, ladle into bowls. Drizzle with more chili oil and chopped basil.