Pre-heat the oven to 400ºF.
Line a baking sheet with aluminum foil.
In a large bowl, whisk together the oil, mustard, brown sugar, vinegar, salt, and pepper.
Add the onion wedges and carrots, then toss to combine.
In a large baking pan, spread the carrots and onions in an even layer and roast in the oven until tender, stirring halfway, about 35 minutes in total.
Stir in the butter, then serve.