In conventional laser-scanning microscopy, images are formed by acquiring the signal from pixel to pixel. Here, we report more than one order of magnitude reduction in acquisition time of Interferometric Second Harmonic Generation (I-SHG) by scanning the phase within each pixel, to characterize the relative polarity of various samples. Using an electro-optic phase-scanner, we show that the phase-shift patterns required for interferometry can be applied at each pixel during the scanning of the sample, allowing single-scan I-SHG (1S-ISHG) measurements. Requiring exposure times comparable to standard SHG intensity images, the additional phase information of the signal can thus be retrieved in parallel to its amplitude at the time-scale of seconds. Moreover, slower modulations can be used to enhance the precision of the phase measurement, without any spatial or temporal shift between interferograms, in contrast to conventional frame phase-shifting I-SHG (standard I-SHG). This continues to extend I-SHG to dynamical processes, and opens it to large-scale studies, as well as to imaging samples where the signal-to-noise ratio is an issue.