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We present measurements of the spatiotemporal evolution of a hot-dense plasma generated by the interaction of an intense 25 fs laser pulse with a solid target, using pump-probe two-dimensional (2D) Doppler spectrometry. Measuring the time-dependent Doppler shifts at different positions across the probe beam, we achieve velocity mapping at hundreds of femtoseconds time resolution simultaneously with a few micrometer spatial resolution across the transverse length of the plasma. Simulations of the interaction using a combination of 2D particle-in-cell and 2D radiation hydrodynamics codes agree well with the experiment.