With the rise of voice-enabled technologies, loudspeaker playback has become widespread, posing increasing risks to speech privacy. Traditional eavesdropping methods often require invasive access or line-of-sight, limiting their practicality. In this paper, we present mmSpeech, an end-to-end mmWave-based eavesdropping system that reconstructs intelligible speech solely from vibration signals induced by loudspeaker playback, even through walls and without prior knowledge of the speaker. To achieve this, we reveal an optimal combination of vibrating material and radar sampling rate for capturing high-quality vibrations using narrowband mmWave signals. We then design a deep neural network that reconstructs intelligible speech from the estimated noisy spectrograms. To further support downstream speech understanding, we introduce a synthetic training pipeline and selectively fine-tune the encoder of a pre-trained ASR model. We implement mmSpeech with a commercial mmWave radar and validate its performance through extensive experiments. Results show that mmSpeech achieves state-of-the-art speech quality and generalizes well across unseen speakers and various conditions.