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Ultrashort laser pulses are essential in advanced research, medicine and industry, but the precise characterization remains challenging. The absolute phase of ultrashort light pulses, the so-called carrier-envelope phase (CEP), enables the control of light-matter interaction in the few cycle regime [1]. Its precise measurement is therefore essential, in particular at single-shot and high repetition rate. With the new class of industrial grade lasers based on Ytterbium- and Thulium-doped materials, repetition rates of hundreds of kHz to MHz are readily available together with CEP-stable and few-cycle versions. We have demonstrated a novel, all-optical method to measure the CEP of ultrashort laser pulses, in single-shot for every laser shot, at a repetition rate of 200 kHz [2]. Here, we extend the parameter space of our technique to 586 kHz, which is the fastest single-shot CEP detection ever performed, to the best of our knowledge.