In a medium deep-sided skillet, arrange the carrots and pour in enough water to cover them completely. Sprinkle in the dried thyme and salt, then bring the water to a rolling boil over medium-high heat. Stir gently and allow the carrots to cook for about 20 minutes until they reach a tender, fork-soft consistency. Carefully drain the cooked carrots and return them to the same skillet. Incorporate the butter and brown sugar, cooking over medium heat for 5 to 6 minutes until the sugar fully dissolves and the carrots acquire a glossy caramelized coating. Season with black pepper and adjust salt to taste. Transfer to a serving dish and garnish generously with fresh chopped parsley.
Instant Pot Method
Add 1 ½ cups water, carrots, thyme, and salt to the Instant Pot. Secure the lid in the sealed position and set to manual, high pressure for 2 minutes. Once finished, perform a quick pressure release, then drain the carrots. Return them to the Instant Pot, add the butter and brown sugar, then activate the sauté function. Cook for 3 to 4 minutes until caramelized, then stir in black pepper and extra salt if needed. Serve with parsley sprinkled over the top.