Integrated combustor nozzles and turbomachines are provided. An integrated combustor nozzle includes a cooling insert having a flange. The cooling insert further includes a first wall and a second wall that each define respective passages therein. The first wall and the second wall each extend from an open end defined within the flange to a closed end. The first wall and the second wall each include an impingement side spaced apart from a solid side. Each impingement side defines a plurality of impingement apertures configured to direct coolant from the respective passage towards a side wall of the combustion liner. The cooling inserts further includes a collection passageway that is defined between the solid sides of the first wall and the second wall.