I'm pretty sure that їм is just the я form of the verb, and that їсти is the infinitive. So, similar to Spanish where when you say "I want to read", it would be (at least I think) "Quiero leer." while "I read" is "Leo."? Although you may understand that already--perhaps їсти is somewhat irregular? I'm not actually sure.
Eta: https://en.m.wikipedia.org/wiki/Ukrainian_grammar#Athematic_verbs looks like їсти is a little unusual in present tense as verbs go.