Add the onion, carrots, parsnips, and potatoes to a large rimmed baking sheet. In a small bowl, whisk together the oil, honey, mustard, salt, and pepper until well combined. Measure out 2 tablespoons of the mixture and set aside for later. Pour the remaining mixture over the veggies, then toss to combine and spread in an even layer.
Bake for about 35 to 40 minutes, stirring once halfway through, until tender and starting to brown. Remove from the oven and let cool for about 2 to 3 minutes.
Drizzle with the reserved 2 tablespoons sauce and toss to combine. Taste and season with additional salt and pepper if needed.