I recently learned about a trope called the katsudan confession. The idea is that when the police have you in for questioning, they will get you a meal in order to make you lower your defenses. This only occurs in fiction, because it is in fact against the rules for the police to bring things to a prisoner or someone being questioned.
In any case, it is something that shows up on TV. And so she is treating Nanami to katsudan in order to Make her more likely to tell the truth about what happened.