Set the oven to 425°F. Line a light-colored rimmed sheet pan with aluminum foil for easy cleanup.
In a large bowl, whisk together the butter, olive oil, balsamic vinegar, salt, pepper, and thyme leaves until blended.
Add the carrots to the bowl and stir until evenly coated.
Spread the carrots in a single layer on the prepared pan, leaving a little space between them for even roasting.
Roast for 40 minutes, until the bottoms are deeply caramelized and the carrots are tender through the center.
Transfer to a serving platter and garnish with additional fresh thyme, and serve warm.