Personalized search represents a problem where retrieval models condition on historical user interaction data in order to improve retrieval results. However, personalization is commonly perceived as opaque and not amenable to control by users. Further, personalization necessarily limits the space of items that users are exposed to. Therefore, prior work notes a tension between personalization and users' ability for discovering novel items. While discovery of novel items in personalization setups may be resolved through search result diversification, these approaches do little to allow user control over personalization. Therefore, in this paper, we introduce an approach for controllable personalized search. Our model, CtrlCE presents a novel cross-encoder model augmented with an editable memory constructed from users historical items. Our proposed memory augmentation allows cross-encoder models to condition on large amounts of historical user data and supports interaction from users permitting control over personalization. Further, controllable personalization for search must account for queries which don't require personalization, and in turn user control. For this, we introduce a calibrated mixing model which determines when personalization is necessary. This allows system designers using CtrlCE to only obtain user input for control when necessary. In multiple datasets of personalized search, we show CtrlCE to result in effective personalization as well as fulfill various key goals for controllable personalized search.