Place the sliced carrots in a medium saucepan and add enough water to cover them by about 1 inch.
Bring the water to a boil over medium-high heat, then reduce the heat to medium and simmer the carrots for 8 to 10 minutes, or until they are just tender when pierced with a fork.
Drain the carrots and set aside.
In the same saucepan, melt the butter over medium heat.
Add the honey and brown sugar to the melted butter, stirring constantly until the sugar dissolves and the mixture is smooth, about 2 minutes.
Add the cooked carrots back to the saucepan and toss to coat them evenly with the honey and brown sugar glaze.
Cook the carrots in the glaze for an additional 5 minutes, stirring occasionally, until the glaze thickens and coats the carrots nicely.
Season with salt and ground black pepper, stirring to combine.
Remove from heat and sprinkle the chopped fresh parsley over the glazed carrots.
Serve warm.