In a large sauce pot, add in the baby carrots, then stir in the pineapple juice and sugar until the sugar is fully incorporated and dissolved. Simmer on the stove for 5-10 minutes.
Add in the arrowroot powder and stir until all of the starch is absorbed. Cover and let simmer and bubble for 10-15 minutes, stirring occasionally.
To the carrots, add in the butter and stir until the butter is melted. Cover again and let simmer for an additional 10 minutes or until the carrots are semi-fork tender.
Notes
Use as big of a pan as you can for the carrots to allow the carrots to soften as they cook down.Add in the pineapple juice and sugar separate from the arrowroot. I've tested this a few times, and adding the arrowroot in after you combine the pineapple juice and sugar keeps it from clumping.To speed up the process, cover the carrots as they simmer, stirring occasionally. This will help it get thick and the carrots to soften.This might sound a little odd, but baby carrots come in various sizes. This will actually matter when you are making this recipe, so be sure to find a package of baby carrots that are not too large, as this will make the recipe take a few minutes longer.