Quantum computing poses a threat to classical cryptography, particularly in key-exchange protocols. This paper introduces a new key-exchange protocol that proposes the integration of the (p,q)-Transform with the BLAKE3 hash function, providing a solution immune to threats posed by quantum computing. The (p,q)-Transform introduces nonlinearity to strengthen security, while BLAKE3 uses the eXtendable Output Function (XOF) to provide strong hashing features that obscure the shared secrets. The performance comparison with other quantum-resistant algorithms such as Kyber 512 and sntrup761 shows that it is highly efficient and consumes much less memory and is a great candidate for a secure quantum-resistant cryptographic key-exchange protocol.