The pasta dough may be made either by hand or in a food processor. After the dough is prepared, it may be rolled out by machine or by hand. I will describe each step highlighting your options.
If you use pre-cooked beets, skip to step 5 here below. If you want to use fresh beets, wash the red beets and remove any greens. Leave the skin on the red beets until after they are cooked.
You have choices on how to cook your red beets: in a pressure cooker, in a pot over the stove or in the oven. If you use a PRESSURE COOKER, put the red beets in a strainer at the bottom of the pressure cooker with enough water to touch the bottom of the strainer. Be careful not to have too little water so the pressure cooker burns. Cook for about 20 minutes after the cooker reaches high pressure. If you use a pot OVER THE STOVE, put the red beets in a pot with a little water over the stove. Bring to a boil and then reduce to a simmer. Let cook about 45 minutes or until soft enough to puree. If you ROAST the red beets, put them in a roasting pan wrapped in baking paper or aluminum foil. Let cook about 45 minutes or until soft enough to puree.
Remove the red beets and let sit about 5 minutes to let cool off. Remove the skins. They should come off easily.
Puree the red beets using a hand mixer, a food processor, or a mashing device.
Put the pureed red beets in a strainer over a bowl to eliminate excess liquid. Press down on the pureed red beets to remove as much liquid as possible. Use the excess liquid in a soup or a smoothie to benefit from the nutrients.
Once the pureed red beets are cool, you can prepare the dough. If you prepare the dough BY HAND, put the pureed red beets with the egg and egg yolks in a large mixing bowl. Add a pinch of salt. Mix together with a wooden spoon. Add one-third of the flour and then mix together. Add another one-third of flour and mix together. Continue mixing with the wooden spoon as you add more flour a bit at a time until the dough begins to separate from the bowl. If you use a FOOD PROCESSOR, add the pureed red beets, the egg and egg yolks, a pinch of salt, and three-fourths of the flour into the food processor bowl. Pulse together about 20 to 30 seconds until the dough begins to separate from the bowl. If it does not separate, add more flour until it comes together in a ball. I needed the indicated amount of flour but the exact quantity may vary according to the amount of liquid in the pureed beets and the size of the eggs used. Note: try not to stretch this step out too long as you do not want to work the dough too much, otherwise the pasta will have more elasticity (be more chewy).
Once the dough starts to separate enough so you can touch the dough with your hands without the dough sticking to them, you can knead the dough a few minutes (2 to 3 minutes) on a wooden board or clean counter. You may need to add a little more flour at this stage to avoid the dough sticking to your hands. Stop adding flour when the dough is soft to the touch and does not stick to your hands.
Divide the ball of dough into 2 or 3 portions. If you like, add a drop of olive oil to your hands and rub it lightly on the outside of the dough. This step is optional. Wrap each portion in plastic film and put in the refrigerator to rest at least 30 minutes.