Cut the carrots crosswise into 2-inch pieces. If they are more than 1-inch thick, halve or quarter them lengthwise into pieces, otherwise, leave them whole.
Melt the butter in a large skillet over medium heat. Once the butter is melted, add the carrots and cook, stirring occasionally, until carrots are tender and butter is browned, 8 to 10 minutes.
Stir in the brown sugar and cook until the brown sugar is dissolved and the carrots are coated and slightly caramelized, about 4 minutes longer. Season with salt and pepper.