A method of forming a cooling assembly in a turbomachine part is provided. The method includes placing an encapsulated diffuser insert partially into a hole in the turbomachine part. The encapsulated diffuser insert has an unobstructed central passageway with a generally circular cross-section at a first end and an elongated rectangular cross-section at a second end opposing the first end. The second end has a sacrificial cap. A coating step coats the turbomachine part to at least partially encapsulate the encapsulated diffuser insert in a coating. A removing step removes the sacrificial cap to enable air flow through the central passageway. The encapsulated diffuser insert remains in the hole of the turbomachine part and the coating, thereby providing the unobstructed central passageway with a generally circular first end and an elongated rectangular second end adjacent to an outer surface of the turbomachine part.