A method is provided for manufacturing at least a portion (24) of a heat exchanger. During this method, a first heat exchanger section (46) is formed that includes a base (28) and a plurality of protrusions (34A,35A,36A). The forming of the first heat exchanger section (46) includes building up at least one protrusion material on the base (28) to form the protrusions (34A,35A,36A). The first heat exchanger section (46) is attached to a second heat exchanger section (52). A plurality of flow channels (38) are defined between the first heat exchanger section (46) and the second heat exchanger section (52).