Either by hand or using a machine, blend the eggs and flour thoroughly. Knead for about 10 minutes. If using a machine, the mixture will most likely look like breadcrumbs at this point. It may look a little dry, but if you can successfully press the crumbs together with your fingers it is sufficiently moist. When you have finished mixing/kneading, press the mixture together if necessary, wrap in clingfilm and rest on the work surface for 30 minutes.
When the pasta is ready to roll, remove the plastic and cut into 4 pieces. Shape each piece into a rough rectangle and feed through a pasta machine about 10 times on thickness setting 1, folding the pasta in two each time you run it through - this effectively re-kneads the pasta and greatly improves the texture.
Continue running the pasta through the machine, raising the thickness setting a stage at a time until you reach the desired thickness. I stopped when I reached setting 6, which for pasta of this dryish texture was about 1mm thick (see picture in the post). I rolled the pasta for this dish fairly thick so it would survive being removed from the water with tongs (see assembly instructions below) and would hold its shape somewhat when layered with the vegetables.
Lay the sheets on a work surface and cut them into neat squares with a sharp knife. I did not need any flour or semolina to roll out or cut my pasta, but if you are at all worried about your pasta sticking, lightly flour it and do not lay sheets on top of each other. Set aside.