Use a sharp knife to diagonally cut the carrots crosswise into 2-inch chunks. If any of the pieces are very thick, cut them in half lengthwise so that all the pieces are a similar thickness.
Melt the butter or heat the olive oil in a large skillet over medium heat. Add the carrots, ½ teaspoon of the salt, and several grinds of pepper. Cook, stirring occasionally, for 5 to 10 minutes, or until the carrots soften slightly.
Add the water to the pan and cook for another 2 minutes, or until the water reduces slightly. Add the brown sugar and continue to cook for 5 to 10 minutes, or until the carrots have softened to your liking and the sugar creates a syrupy glaze.
Remove from the heat, add the garlic and the remaining ¼ teaspoon salt, and toss to incorporate. Add the lemon juice, toss again, and season to taste with more lemon, salt, and pepper as desired.