Set the oven to 400°F (204°C) to preheat. Line a large baking sheet with parchment paper and set aside.
Wash the carrots well, and peel if desired. Using a sharp knife, trim off the ends and cut the larger vegetables from top to bottom and lengthwise, creating pieces that are about 3 inches long and 1 inch thick at the thickest point. Transfer the pieces into a large bowl.
Add the oil, honey, honey mustard, thyme leaves, vinegar, and salt to a small bowl, then whisk or stir with a spoon to fully combine.
Pour the mixture into the bowl with carrots and parsnips. Using tongs or your hands, toss the vegetables until they're coated well on all sides.
Arrange the coated veggies in a single layer on the prepared baking sheet. Drizzle any of the remaining honey mixture from the bowl over the vegetables.
Bake in preheated oven for 35-40 minutes until fork tender, stopping halfway to turn the pieces over.
Remove from the oven, then transfer to a serving platter.
Notes
Store leftovers in an airtight container in the refrigerator and use within 3-4 days.For best flavor and texture, choose carrots that are medium in size, about 6-9 inches long, and under 2 inches in diameter at the thickest point.To Make Ahead: Up to 5 days in advance, prepare the honey mixture and store in a covered container in the refrigerator. Wash and prep the vegetables and refrigerate them in a storage container.Instructions to make this recipe in an air fryer are in the FAQ section of the blog post.