Cook squash in a large pot of simmering (not boiling) salted water 6 minutes. Add cauliflower; continue simmering until vegetables are very tender, 10 to 12 minutes more. Drain, then return vegetables to pot. Cook over medium heat, stirring frequently, until vegetables appear dry and a film forms on bottom of pot, 3 to 4 minutes. Pass vegetables through a ricer, food mill, or chinois strainer; cover to keep warm.Advertisement
Heat oil in a saucepan over medium. When it shimmers, add ginger and garlic; cook until fragrant and sizzling, about 30 seconds. Add coconut milk; season with salt and pepper. Bring to a simmer, then remove from heat and stir into vegetable mixture until smooth. If mash is too stiff, add broth or water, a few tablespoons at a time. Season with salt and pepper and serve warm.