Slavonian food is among the heartiest in Croatia — this is kulen country, and meals tend to involve cured pork, paprika, and plenty of it. The kulen sausage (fiery and slow-cured) is the thing to try; the best versions come from local farms and are sold at the city market. Fish from the Drava and Danube — catfish, carp, perch — appears on almost every menu, usually as a paprikaš (a spiced stew) or on the grill.
Slavonska Kuća on Kamila Firingera is the most reliable place for traditional Slavonian cooking: the fixed menu changes daily around local produce and seasonal game. Cafes and cake shops are a strong point in Osijek — the central European coffee culture is alive here in a way it isn't on the Dalmatian coast. Try Waldinger's, next to the gallery of the same name.