Heat oil in a large pot over medium heat; cook and stir onion until fragrant, 1 minute. Add cauliflower and cover. Cook, stirring occasionally, until slightly tender, 10 minutes. Add chicken stock, ginger, and salt; season with black pepper. Bring to a boil, cover, and simmer until cauliflower is tender, 30 minutes. Cool slightly.
Pour soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Return to pot and warm over low heat. Serve immediately.