When we speak, we not only make movements with our mouth, lips, and tongue, but we also hear the sound of our own voice. Thus, speech production in the brain involves not only controlling the movements we make, but also auditory and sensory feedback. Auditory responses are typically suppressed during speech production compared to perception, but how this manifests across space and time is unclear. Here we recorded intracranial EEG in seventeen pediatric, adolescent, and adult patients with medication-resistant epilepsy who performed a reading/listening task to investigate how other auditory responses are modulated during speech production. We identified onset and sustained responses to speech in bilateral auditory cortex, with a selective suppression of onset responses during speech production. Onset responses provide a temporal landmark during speech perception that is redundant with forward prediction during speech production. Phonological feature tuning in these "onset suppression" electrodes remained stable between perception and production. Notably, the posterior insula responded at sentence onset for both perception and production, suggesting a role in multisensory integration during feedback control.