Place the parsnips and carrots into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, 15 to 20 minutes. Drain; return vegetables to pot. Turn heat to low, stir in the chives and 3 tablespoons of butter.
Begin to puree mixture using an immersion blender. Add 3 tablespoons of butter and continue to puree until mixture is smooth. Season with salt and pepper to taste.
164.3 calories; 0.51 g protein; 2.65 g carbohydrates; 0.99 g dietary-fiber; 1.12 g sugars; 17.35 g fat; 10.95 g saturated-fat; 45.8 mg cholesterol; 5857.94 IU vitamin-a-iu; 0.31 mg niacin-equivalents; 0.05 mg vitamin-b6; 2.84 mg vitamin-c; 8.06 mcg folate; 17.05 mg calcium; 1.11 mg iron; 5.99 mg magnesium; 86.32 mg potassium; 220.47 mg sodium; 0.01 mg thiamin; 156.18 calories-from-fat; 6 percent-of-calories-from-carbs; 92 percent-of-calories-from-fat; 1 percent-of-calories-from-protein; 58 percent-of-calories-from-sat-fat