Coronagraphy is a powerful technique to achieve high contrast imaging and hence to image faint companions around bright targets. Various concepts have been used in the visible and near-infrared regimes, while coronagraphic applications in the mid-infrared remain nowadays largely unexplored. Vector vortex phase masks based on concentric subwavelength gratings show great promise for such applications. We aim at producing and validating the first high-performance broadband focal plane phase mask coronagraphs for applications in the mid-infrared regime, and in particular the L band with a fractional bandwidth of ~16% (3.5-4.1 mu m). Based on rigorous coupled wave analysis, we designed an annular groove phase mask (AGPM) producing a vortex effect in the L band, and etched it onto a series of diamond substrates. The grating parameters were measured by means of scanning electron microscopy. The resulting components were then tested on a mid-infrared coronagraphic test bench. A broadband raw null depth of 2 x 10^{-3} was obtained for our best L-band AGPM after only a few iterations between design and manufacturing. This corresponds to a raw contrast of about 6 x 10^{-5} (10.5 mag) at 2lambda/D. This result is fully in line with our projections based on rigorous coupled wave analysis modeling, using the measured grating parameters. The sensitivity to tilt and focus has also been evaluated. After years of technological developments, mid-infrared vector vortex coronagraphs finally become a reality and live up to our expectations. Based on their measured performance, our L-band AGPMs are now ready to open a new parameter space in exoplanet imaging at major ground-based observatories.