Motivation: The SARS-CoV-2 pandemic has emphasised the importance of developing a universal vaccine that can protect against current and future variants of the virus. Results: The present study proposes a novel conditional protein Language Model architecture, called Vaxformer, which is designed to produce natural-looking antigenicity-controlled SARS-CoV-2 spike proteins. We evaluate the generated protein sequences of the Vaxformer model using DDGun protein stability measure, netMHCpan antigenicity score, and a structure fidelity score with AlphaFold to gauge its viability for vaccine development. Our results show that Vaxformer outperforms the existing state-of-the-art Conditional Variational Autoencoder model to generate antigenicity-controlled SARS-CoV-2 spike proteins. These findings suggest promising opportunities for conditional Transformer models to expand our understanding of vaccine design and their role in mitigating global health challenges.