Preheat the oven to 425°F (220°C). Arrange the carrots in a single layer in a large, shallow baking dish.
In a small bowl, whisk together the melted butter, bourbon, light brown sugar, kosher salt, and black pepper until smooth.
Pour the mixture evenly over the carrots, making sure they are well coated. Spread them into an even layer.
Roast the carrots for 45–55 minutes, turning them occasionally to ensure they stay coated in the sauce, until they are tender. Adjust the cooking time if needed based on the size of the carrots.
Remove the baking dish from the oven and transfer the carrots to a serving platter.
Sprinkle chopped parsley on top before serving.