Various methods and systems are provided for an exhaust gas recirculation (EGR) EGR cooler for an engine system. In one example, the EGR cooler includes a first section with a first group of tubes adapted to flow exhaust gases, and also includes a first group of passages formed by exterior surfaces of the first group of tubes and adapted to flow coolant from a coolant source. The EGR cooler also includes a second section including a second group of tubes adapted to flow coolant from the coolant source, and a second group of passages formed by exterior surfaces of the second group of tubes and adapted to flow the exhaust gas from the first group of tubes.