Free electron beams that carry high values of orbital angular momentum (OAM) possess large magnetic moments along the propagation direction. This makes them an ideal probe for measuring the electronic and magnetic properties of materials, as well as for fundamental experiments in magnetism. However, their generation requires the use of complex diffractive elements, which usually take the form of nano-fabricated holograms. Here, we show how the limitations of the current fabrication of such holograms can be overcome by using electron beam lithography. We demonstrate experimentally the realization of an electron vortex beam with the largest OAM value that has yet been reported to the first diffraction order (L = 1000 ℏ), paving the way for even more demanding demonstrations and applications of electron beam shaping.