Face recognition has attracted increasing attention due to its wide range of applications, but it is still challenging when facing large variations in the biometric data characteristics. Lenslet light field cameras have recently come into prominence to capture rich spatio-angular information, thus offering new possibilities for advanced biometric recognition systems. This paper proposes a double-deep spatio-angular learning framework for light field based face recognition, which is able to learn both texture and angular dynamics in sequence using convolutional representations; this is a novel recognition framework that has never been proposed before for either face recognition or any other visual recognition task. The proposed double-deep learning framework includes a long short-term memory (LSTM) recurrent network whose inputs are VGG-Face descriptions that are computed using a VGG-Very-Deep-16 convolutional neural network (CNN). The VGG-16 network uses different face viewpoints rendered from a full light field image, which are organised as a pseudo-video sequence. A comprehensive set of experiments has been conducted with the IST-EURECOM light field face database, for varied and challenging recognition tasks. Results show that the proposed framework achieves superior face recognition performance when compared to the state-of-the-art.