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We develop a doubly periodic version of the Simple Convection‐Permitting E3SM Atmosphere Model (SCREAM) to provide an efficient configuration for this global convection permitting model (GCPM), akin to a single column model often found in conventional general circulation models. The design details are explained, in addition to the extensive case library associated with the doubly periodic SCREAM (DP‐SCREAM) configuration. We demonstrate that doubly periodic cloud resolving models are useful tools to explore the horizontal resolution sensitivity of GCPMs, in addition to replicating biases seen in the global models. Using DP‐SCREAM, we show that SCREAM exhibits behaviors of a scale aware model as it is able to naturally partition between sub‐grid scale (SGS) and resolved vertical transport across the gray zone of turbulence. We show that SCREAM is reasonably scale insensitive when run at resolutions from 1 to 5 km, but can exhibit sensitivity, particularly for the shallow convective regime, when run at resolutions approaching that of large eddy simulations. We conclude that SGS parameterization improvements are likely needed to reduce this scale sensitivity. Plain Language Summary: Advances in computational resources have allowed climate simulations to be performed with very high resolution, which provides higher quality results. However, these simulations require a lot of time and computer resources to perform, which makes these models difficult to use for the common scientist. In this paper we develop a high‐resolution configuration which focuses on a specific point on the globe, enabling it to run fast and to use minimal computational resources. This allows users and developers to gauge how the model may perform before doing a computationally intensive global simulation. We show that this faster configuration is a useful tool to replicate problems that are found in the global model and is a valuable way to assess sensitivities of the model, particularly pertaining to choices made in its resolution. Key Points: Doubly periodic configurations represent an efficient framework to supplement global cloud resolving modelsShallow convection is sensitive to horizontal resolution in Simple Convection‐Permitting E3SM Atmosphere Model (SCREAM) but stratiform clouds are more robustSCREAM exhibits the behaviors of a scale aware model and can represent a range of cloud regimes [ABSTRACT FROM AUTHOR]