Melt 3 tablespoons butter in a large pot or Dutch oven over medium heat; cook, stirring occasionally, until browned, about 5 minutes. Add the sweet potatoes, parsnips, thyme sprigs, nutmeg, 1 teaspoon salt and a few grinds of pepper. Cook, stirring, until the vegetables are well coated.
Add 1/2 cup water and the half-and-half to the pot, cover and bring to a simmer. Reduce the heat to medium low and cook, stirring occasionally and adding 1/4 cup more water at a time if the pot is dry, until the vegetables are very tender, 30 to 35 minutes (at the end, there will not be a lot of liquid left).
Discard the thyme sprigs and transfer the vegetables and any liquid to a food processor. Add the remaining 3 tablespoons butter and process until very smooth. Add the vinegar and process to combine; season with salt and pepper. Transfer the potatoes to a serving dish. Sprinkle with more nutmeg.