Controllable Depth-of-Field (DoF) imaging commonly produces amazing visual effects based on heavy and expensive high-end lenses. However, confronted with the increasing demand for mobile scenarios, it is desirable to achieve a lightweight solution with Minimalist Optical Systems (MOS). This work centers around two major limitations of MOS, i.e., the severe optical aberrations and uncontrollable DoF, for achieving single-lens controllable DoF imaging via computational methods. A Depth-aware Controllable DoF Imaging (DCDI) framework is proposed equipped with All-in-Focus (AiF) aberration correction and monocular depth estimation, where the recovered image and corresponding depth map are utilized to produce imaging results under diverse DoFs of any high-end lens via patch-wise convolution. To address the depth-varying optical degradation, we introduce a Depth-aware Degradation-adaptive Training (DA2T) scheme. At the dataset level, a Depth-aware Aberration MOS (DAMOS) dataset is established based on the simulation of Point Spread Functions (PSFs) under different object distances. Additionally, we design two plug-and-play depth-aware mechanisms to embed depth information into the aberration image recovery for better tackling depth-aware degradation. Furthermore, we propose a storage-efficient Omni-Lens-Field model to represent the 4D PSF library of various lenses. With the predicted depth map, recovered image, and depth-aware PSF map inferred by Omni-Lens-Field, single-lens controllable DoF imaging is achieved. Comprehensive experimental results demonstrate that the proposed framework enhances the recovery performance, and attains impressive single-lens controllable DoF imaging results, providing a seminal baseline for this field. The source code and the established dataset will be publicly available at https://github.com/XiaolongQian/DCDI.