In a small saucepan, melt the butter over medium heat. Continue cooking until it turns golden brown and has a nutty aroma. Keep a close eye on it to prevent burning!
Once browned, immediately remove it from the heat and stir in the brown sugar, salt, and black pepper. Let this mixture cool slightly.
Place the carrots into the slow cooker and pour the brown butter mixture over them. Stir to coat the carrots evenly.
If using, sprinkle the thyme or rosemary over the top.
Cover and cook on low for 4-5 hours, or until the carrots are tender to your liking.
Once done, give the carrots a gentle stir. Garnish with fresh parsley before serving, if desired.