Learn Turkish: Bankamatiğe uğramışken şarküteriden peynir de al. - Since you have dropped by the ATM, buy some cheese from the delicatessen too.

Adding just -(y)ken to the present tense (uğrarken) means 'while dropping by', focusing on two actions happening at the exact same moment. The -mIşken pattern used here shows that a state has already been achieved (you went to the ATM and are currently there), which creates a convenient opportunity. It translates best to 'Since you are already there, take the opportunity to...'

Why does the word for ATM take the dative case ending in bankamatiğe?

The verb uğramak (to drop by, to stop by) dictates that the destination must be in the dative (direction) case. You are grammatically saying 'dropped by to the ATM'. Also, note that adding the vowel suffix -e causes the final hard consonant k in bankamatik to soften to a ğ.

Why is the particle de (too/also) used here if cheese is the only item being bought?

The de here doesn't mean buying cheese in addition to other groceries. Instead, it pairs perfectly with the opportunistic -mIşken clause to mean 'In addition to your primary errand at the ATM, do this errand too.'

Is şarküteri the standard word for a grocery store or supermarket?