Common assumption is that cooking plant based iron in olive oil helps absorption because fat aids nutrient uptake. True for fat soluble vitamins but iron works differently.
Polyphenols in EVOO bind to iron in the gut and form a compound the body can't absorb. Same basic mechanism as tea and coffee blocking iron. So the oil is not neutral here.
Some researchers think this is actually part of why the Mediterranean diet is cardioprotective. Excess iron generates oxidative stress and moderating absorption through polyphenols might be contributing to that benefit. Still digging into this one so not making any claims.
If you're iron deficient and eating mostly plant sources, vitamin C is still the better pairing for absorption.