Fresh pasta recipes are generally not vegan friendly, but that's an easy problem to get around. Just eliminate the eggs altogether or use adequate substitutes that don’t contain any animal derivatives.
Yes to pasta, no to eggs
Emilians and Northern Italians always make fresh pasta by adding one large egg for every four ounces of flour. Though Ligurians and Tuscans, ahead of their time, have been making fresh vegan pasta varieties for ages. Trofie and pici, for example, contain only water and flour. Puglia’s orecchiette or strascinati, Sardinia’s maloreddus, and Sicily’s cavatelli, are all egg-free and made with semolina or durum wheat flour instead of soft wheat.
Making fresh vegan pasta
Mix 3 cups of flour (or semolina) with about 1 cup of water, a pinch of salt, and 1 Tbsp. extra-virgin olive oil. If you want to give your pasta a nice warm color as if it contained eggs, you can add a pinch of turmeric or saffron to the flour. As per tradition, place the flour in a heap or fountain-shape on a pastry board, or in a large bowl. Make a small hollow in the center, then pour in the oil, salt, and a little water. Begin to knead with your fingertips, slowly incorporating the flour towards the center. Add the remaining water little by little, continuing to knead until the dough is smooth, soft, firm, and not sticky. Then transfer it to a bowl, cover, and let it rest for 30 minutes outside the fridge. After the resting time, you can roll out the dough into your preferred shape. If the dough is too dry, just moisten your hands and continue working it until it softens.
Cooking vegan pasta
Like any other pasta, fresh vegan pasta should be cooked in plenty of boiling salted water. Fresh pasta generally needs more salt while cooking. Usually, it takes about 5 to 8 minutes to cook, but the best way to check the consistency is to taste it while it cooks. This rule applies to every kind of pasta, even if it entails the risk of eating half of one's portion directly from the pot.