Preheat the oven to 400°F (200°C). Adjust the oven rack to the middle position and line a rimmed baking sheet with foil.
Place the carrots and/or parsnips on the foil, drizzle with the oil, and toss to coat. Spread in a single layer and sprinkle generously with salt and pepper.
Roast the vegetables, turning once, until they’re tender and, if desired, slightly charred, 30 to 40 minutes.
While the vegetables are roasting, in a small saucepan over medium heat, melt the butter. Add the garlic and cook until fragrant, about 1 minute.
Stir in the bourbon, maple syrup, and vinegar, and cook until the glaze thickens enough to coat the back of a spoon, 5 to 10 minutes.
Drizzle half of the glaze over the vegetables, return to the oven, and roast until the glaze bubbles, 3 to 5 minutes.
Transfer the vegetables to a platter and drizzle with the remaining glaze. Serve hot, warm, or room temperature.