Boil the Vegetables: Place the peeled, chopped turnips and celery root in a large stockpot, then add enough water to completely cover the vegetables.
Cook Until Tender: Set the pot over high heat and bring the water to a boil. Continue boiling for 35–45 minutes, or until the turnips and celery root are fork tender. Drain Thoroughly: Drain the cooked vegetables well, removing as much excess water as possible.
Combine the Ingredients: Transfer the drained turnips and celery root to a large mixing bowl. Add the heavy cream, butter, sour cream, salt, nutmeg, and pepper. Mash Until Smooth: Use a potato masher or electric mixer to mash or beat the mixture until smooth and thoroughly combined.
Serve Immediately: Serve the mashed turnips while warm. If desired, finish with additional butter or a light sprinkle of nutmeg.