Boiled carrots are very straight-forward and easy, but the time they take will fluctuate depending on how you prep them, as you'll see below.
This is NOT my preferred way to make carrots, but it might work perfectly for you and the outcome you're searching for as you create your own recipe.
Submerge trimmed, whole carrots in enough boiling water to cover. Adjust the heat as needed to keep the water at a simmer as they cook, covered. They will take anywhere from 45 minutes to 1 1/2 hours, depending on their size.
Or cut the carrots into chunks to drastically cut down on the cooking time. Count on 20-25 minutes.
Baby carrots usually cook up in about 10 minutes. Cute!
Drain and let cool.
Carrots can be chopped, sliced or diced at this point.