Preheat your oven to 400°F. Melt the 4 tbsp. of butter in a small saucepan. Once the butter has melted, turn the heat down as low as it can go. Add the 2 tbsp. of honey, mixing it into the butter as it dissolves. Next, stir in the 2 tsp. of brown sugar and ½ tsp. of salt. Turn off the heat.
Coat the peeled carrots in the butter mixture. I did this by putting the carrots on a tray and pouring the mixture over them, rolling them around in it. Put the carrots on a baking-paper-lined tray. Pour the remaining butter mixture over the top of the carrots.
Put the tray into the oven. Let the carrots cook for about 30 minutes, depending on the size of your carrots. About 5 minutes before they're done, take the tray out of the oven and sprinkle on the ¼ cup of parmesan cheese. To ensure the carrots are done, poke them with a fork to see if they're tender. Enjoy!