Abstract: Real-time embodied companion interaction requires a robot to infer user intent from streaming speech, generate timely responses, and execute expressive, interruptible motions. Existing systems typically decouple dialogue orchestration from gesture synthesis, relying on offline motion generation from complete audio. This separation leaves open how a deployed robot can dynamically synchronize response content, prosodic timing, and physical safety under incremental inputs and uncertain turn boundaries. We present MIRA, a unified framework for full-duplex embodied companion interaction. Given streaming user speech, dialogue history, and vocal affect, MIRA predicts both the response text and an explicit embodiment cue. Discrete social behaviors (\eg listening, greeting) are mapped to validated robot trajectories, while open-ended speaking is paired with streaming, co-speech motion. This generative motion is governed by a predict-more-than-commit sliding window that provides temporal look-ahead for motion continuity while limiting physical commitment to a short, cancellable prefix. Crucially, we design CORTEX, a dual-timescale interaction policy that manages low-latency streaming and deliberative turn decisions, backed by a robot-side execution layer that enforces physical safety constraints at the control rate. We deploy MIRA on an Astribot S1 humanoid robot. Quantitative evaluations demonstrate competitive audio-motion alignment relative to state-of-the-art motion-generation baselines, while real-robot deployment measurements characterize streaming responsiveness and interruption handling.