have you tried these? they’re called tortas de aceite or olive oil wafers, and yes, they are made with a fair amount of olive oil. but, don’t let that scare you. they’re lighter than other pastries.
they originated in andalusia, in seville specifcally. they’re comprised of wheat flour, olive oil and anise, and often other ingredients are added, such as almonds or (my favourite) crystallized sevillan orange.