Using an immersion blender, finely purée the beets. Make sure that there are no large chunks left, as those can create holes in the dough. Tip the flour onto your work surface and use a little bowl to create a well in the center. Crack the eggs into the well and add the puréed beets. Using a fork, scramble the eggs and combine them with the beets.

Then, start to incorporate some flour from the edges and mix until a thick paste forms in the center. Use a bench scraper to fold in the remaining flour until everything comes together into a shaggy dough. Thoroughly knead the dough for about 10 minutes until it feels smooth and elastic. Tightly wrap it in cling film and let it rest for at least one hour at room temperature.

Cut off about half of the dough and keep the rest well wrapped. Roll the dough piece out into a thin pasta sheet: Lightly flour the dough on both sides and pass it through the widest setting of your pasta machine. Fold it in half and run it through the same setting again. Repeat this step until the dough has the same width as the pasta machine. Then, pass it through each subsequent setting until you get to your desired thickness (setting 6 works well for most pasta shapes).