Oddly easier having first dealt with revolutionary Big Mac ingredient (9,6)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

1st, 3rd and 5th letters of ( Oddly ) “ easier ” placed after ( having first ) [ PROCESSED(dealt with/handled, as with a claim, say) + CHE(Guevara, Argentinian revolutionary) ].