Heat a skillet (large enough to hold carrot halves in a single layer) over medium-high heat and add butter.
When butter has melted, add coriander and caraway seeds and toss to coat with the butter. Toast for a minute.
Add carrot halves and toss to coat with the butter. Season with salt and add the brown sugar.
Continue cooking over medium heat until the sugar dissolves and coats the carrots, about 1 minute. Add beer and continue cooking until carrots are tender when pierced with the tip of a knife, 25 to 30 minutes. (If beer cooks down, add a little water to finish cooking.)