Embodiments of the present disclosure include a gas turbine shroud assembly. The shroud assembly may include a shroud structure that defines a first cooling chamber and a second cooling chamber. The shroud assembly may also include a first impingement plate disposed within the first cooling chamber and a second impingement plate disposed within the second cooling chamber. Further, the shroud assembly may include one or more cooling channels formed within the shroud structure. The cooling channels may be configured to connect the first cooling chamber with the second cooling chamber. The shroud assembly may also include a flow of cooling air in communication with the first cooling chamber. In this manner, the flow of cooling air may flow from the first cooling chamber to the second cooling chamber by way of the one or more cooling channels.