The word "peeling" refers to the act of removing the outer layer or skin of something, like a fruit or vegetable, usually done by hand or using a tool. Full definition
I'll keep my eyes peeled for when things go on sale to buy, I think I would be okay with the dresses if they weren't full price. (missamymay.com)
Whenever a major international film festival announces its lineup, we keep our eyes peeled for fresh projects from our favorite filmmakers. (criterion.com)
A generous heap of orange peel makes a wonderful difference too. (smittenkitchen.com)