Translate the scenario into what physiological variable failed: the patient was conscious enough to register and remember the operation, meaning the depth of anaesthesia (her level of hypnosis) was too light. The right monitor is therefore one that quantifies depth of anaesthesia rather than oxygenation, ventilation, or blood flow. The Bispectral index does exactly that. It takes the raw electroencephalogram, processes it, and condenses it into a single value on a 0 to 100 scale, where a band of about 40 to 60 corresponds to surgical general anaesthesia and makes accidental awareness unlikely. Test the distractors against this requirement. Pulse oximetry tells us about arterial oxygen saturation and heart rate, not wakefulness. Colour Doppler is an ultrasound technique for visualising blood flow in vessels, irrelevant to consciousness. End tidal carbon dioxide reflects adequacy of ventilation and confirms the airway and circuit, again not depth. Only BIS targets the parameter at fault. So intraoperative awareness is evaluated and minimised using the bispectral index. $Bispectral\ index$ is the monitor of choice.\[\boxed{\text{Bispectral index}}\]