To begin, combine the brown sugar, water, and orange juice in a pot. Bring it to a boil, reduce the heat, and keep the liquid nice and hot.
Wash, peel, and wash the carrots a second time.
Cut the carrots into 3 inch pieces, splitting the larger pieces so that they are all similar in thickness.
Arrange the carrots into your clean, hot jars, packing them in tightly. Leave a 1 inch head space.
Ladle in the hot glazing liquid. Use a bubble wand to remove air pockets. Add more liquid if needed to maintain the 1 inch of head space.
Wipe the rims with a damp rag dipped in white vinegar. Place a lid and ring on the jar and set it in your pressure canner. Repeat with all of the carrots and jars.
Pressure can the carrots for 30 minutes at 10lb pressure. (The time is the same for pints or quarts.) Adjust this for higher elevations.
Notes
The processing time and pressure is for 0-1,000 ft elevation. See your canner's user manual to learn how to adjust the time and pressure for your elevation if you live at a higher altitude.