Bring a large pot of salted water to a boil over high heat. Add the parsnips and cook until they begin to soften, 6 to 7 minutes. Add the cauliflower florets and continue boiling until both the parsnips and the cauliflower are fork-tender, 9 to 11 minutes more. If the water starts boiling over, reduce the heat to medium.
Drain the cauliflower and parsnips in a colander. Let cool slightly, about 3 minutes, then transfer the vegetables to a blender or food processor. Add the milk, butter, garlic powder, the 1½ teaspoons salt, and the black pepper and blend (with the steam vent open on the blender top) on high speed until completely smooth, 45 to 60 seconds. If the puree is too thick, add more milk by the tablespoon to thin. Season to taste with salt.
Transfer the puree to a shallow bowl and serve.
