In this paper we propose a novel virtual simulation-pilot engine for speeding up air traffic controller (ATCo) training by integrating different state-of-the-art artificial intelligence (AI)-based tools. The virtual simulation-pilot engine receives spoken communications from ATCo trainees, and it performs automatic speech recognition and understanding. Thus, it goes beyond only transcribing the communication and can also understand its meaning. The output is subsequently sent to a response generator system, which resembles the spoken read-back that pilots give to the ATCo trainees. The overall pipeline is composed of the following submodules: (i) an automatic speech recognition (ASR) system that transforms audio into a sequence of words; (ii) a high-level air traffic control (ATC)-related entity parser that understands the transcribed voice communication; and (iii) a text-to-speech submodule that generates a spoken utterance that resembles a pilot based on the situation of the dialogue. Our system employs state-of-the-art AI-based tools such as Wav2Vec 2.0, Conformer, BERT and Tacotron models. To the best of our knowledge, this is the first work fully based on open-source ATC resources and AI tools. In addition, we develop a robust and modular system with optional submodules that can enhance the system's performance by incorporating real-time surveillance data, metadata related to exercises (such as sectors or runways), or even a deliberate read-back error to train ATCo trainees to identify them. Our ASR system can reach as low as 5.5% and 15.9% absolute word error rates (WER) on high- and low-quality ATC audio. We also demonstrate that adding surveillance data into the ASR can yield a callsign detection accuracy of more than 96%.