Essential tremor (ET) is a prevalent movement disorder characterized by marked clinical heterogeneity. Here, we explored the morphometric underpinnings of this cross-subject variability on a cohort of 34 patients with right-dominant drug-resistant ET and 29 matched healthy controls (HCs). For each brain region, group-wise morphometric data was modelled by a multivariate Gaussian to account for morphometric features' (co)variance. No group differences were found in terms of mean values, highlighting the limits of more basic group comparison approaches. Variance in surface area was higher in ET in the left lingual and caudal anterior cingulate cortices, while variance in mean curvature was lower in the right superior temporal cortex and pars triangularis, left supramarginal gyrus and bilateral paracentral gyrus. Heterogeneity further extended to the right putamen, for which a mixture of two Gaussians fitted the ET data better than a single one. Partial Least Squares analysis revealed the rich clinical relevance of the ET population's heterogeneity: first, increased head tremor and longer symptoms' duration were accompanied by broadly lower cortical gyrification. Second, more severe upper limb tremor and impairments in daily life activities characterized the patients whose morphometric profiles were more atypical compared to the average ET population, irrespective of the exact nature of the alterations. Our results provide candidate morphometric substrates for two different types of clinical variability in ET. They also demonstrate the importance of relying on analytical approaches that can efficiently handle multivariate data and enable to test more sophisticated hypotheses regarding its organization.