Initial Preparation of Carrots: Commence by placing the baby carrots and the designated water volume into a large skillet. Turn the heat to medium-high and await the water's transition to a simmering point. Subsequently, integrate the salt and stir intermittently, ensuring uniformity in the cooking process. This phase is completed when the water has fully evaporated and the carrots exhibit an initial softening.

Sauce Creation: At this juncture, introduce the unsalted butter, pure honey, and packed light brown sugar to the skillet. Continuous stirring is paramount to ensure the sugars appropriately integrate into the butter. Maintain this process for an additional 5 minutes, or until the amalgamation has thickened into a glaze consistency and the carrots can be effortlessly pierced with a fork.

Final Seasoning and Presentation: Once the carrots are sufficiently glazed, it is prudent to taste and adjust seasoning as per individual preference, incorporating additional salt and black pepper as required. To finalize, sprinkle the freshly chopped dill throughout the skillet and stir thoroughly, ensuring the herb is evenly distributed.