The increasing availability of ultra-high field scanners has led to a growing number of submillimetre fMRI studies in humans, typically targeting the gray matter at different cortical depths. In most analyses, the definition of surfaces at different cortical depths is based on an anatomical image with different contrast and distortions than the functional images. Here, we introduce a novel sequence providing bias-field corrected T1-weighted images and T1-maps with distortions that match those of the fMRI data, with an image acquisition time significantly shorter than standard T1-weighted anatomical imaging. For 'T1-imaging with 2 3D-EPIs', or T123DEPI, 3D-EPI volumes are acquired centred at two inversion times. These 3D-EPIs are segmented into half, quarter or smaller blocks of k-space to allow for optimisation of the inversion times. T1-weighted images and T1-maps are then generated as for MP2RAGE acquisitions. A range of T123DEPI data acquired at 7 T is shown with resolutions ranging from 0.7 mm to 1.3 mm isotropic voxels. Co-registration quality to the mean EPI of matching fMRI timecourses shows markedly less local deviations compared to co-registration of a standard MP2RAGE to the same echo planar volume. Thus, the T123DEPI T1-weighted images and T1-maps can be used to provide cortical surfaces with matched distortions to the functional data or else to facilitate co-registration between functional and undistorted anatomical data.