In this paper, we introduce DA$^2$, the first large-scale dual-arm dexterity-aware dataset for the generation of optimal bimanual grasping pairs for arbitrary large objects. The dataset contains about 9M pairs of parallel-jaw grasps, generated from more than 6000 objects and each labeled with various grasp dexterity measures. In addition, we propose an end-to-end dual-arm grasp evaluation model trained on the rendered scenes from this dataset. We utilize the evaluation model as our baseline to show the value of this novel and nontrivial dataset by both online analysis and real robot experiments. All data and related code will be open-sourced at https://sites.google.com/view/da2dataset.