Heat vegetable oil in a 4-quart pot with a tight-fitting lid over medium-low heat. Cook and stir vegetables in the hot oil until nearly tender, 7 to 10 minutes; add garlic and cook until fragrant, about 1 minute more.
Stir cauliflower and carrot into the vegetable mixture; season with allspice and seasoned salt. Pour vegetable broth over the vegetable mixture. Place lid on the pot and cook vegetables until soft, 30 to 45 minutes.
Ladle about half the vegetables into the bowl of a blender with enough liquid to cover. Hold lid in place with a towel and pulse blender a few times to get mixture moving before leaving blender on to puree vegetables entirely.
Mash remaining vegetables in the pot with a fork or potato masher until no large chunks remain. Pour pureed vegetable mixture into the pot with the coconut milk; stir. Season soup with salt and pepper.
