Place racks in middle and lower third of oven; preheat to 400°. Line 2 large rimmed baking sheets with foil. Divide 2 lb. medium carrots, peeled, halved lengthwise, and 2 lb. medium parsnips, peeled, halved lengthwise, between baking sheets and spread out in a single layer on each. Drizzle 6 Tbsp. extra-virgin olive oil over carrot-parsnip mixture, dividing evenly, and season generously with kosher salt and freshly ground black pepper; toss to coat.
STEP 2
Roast carrots and parsnips, tossing every 10 minutes or so and rotating baking sheets top to bottom halfway through, until tender and browned in spots, 35–40 minutes.
STEP 3
Melt 1 Tbsp. plus 1½ tsp. unsalted butter in a small saucepan over medium heat. Add 1 Tbsp. plus ½ tsp. honey and 1 tsp. balsamic vinegar; stir to combine.
STEP 4
To serve, transfer roasted vegetables to a platter or medium bowl, drizzle honey glaze over, and toss to coat. Do Ahead: Roasted carrots and parsnips can be cooked 2 hours ahead. Tent with foil and let stand at room temperature. Reheat, uncovered, in a 350° oven until warmed through, 8–10 minutes.