• On a clean work surface or in a mixing bowl, form a mound with the flour, and create a well in the center. Into the well, add the eggs, salt, olive oil, and water.
• With a fork, lightly whisk the eggs, gradually incorporating the flour from the inner edges of the mound. Use your other hand to gently cup the flour, maintaining the mound's shape as you work. Once the mixture begins to come together, transition to kneading the dough with the palms of your hands. Avoid forcing all the flour into the dough; incorporate just enough until it forms a cohesive, non-sticky ball.
• If the dough absorbs all the flour but remains sticky, sprinkle in additional flour a little at a time. Continue kneading for about 10 minutes—this step is essential to achieving a smooth, pliable dough. When the dough is soft and elastic, wrap it tightly in plastic wrap to prevent drying out and let it rest for 30 minutes.

For Pasta Machine Method:

• After the dough has rested, divide it into four equal parts. Keep three portions wrapped while working on one. Shape the piece into a rectangle with your hands. Set your pasta machine to its widest setting and roll the dough through.
• Fold the dough in half and pass it through the widest setting again. Repeat this folding and rolling process two more times. Gradually reduce the machine’s settings, rolling the dough thinner each time until you reach the desired thickness.
• Attach the tagliatelle cutter to the machine and feed the dough through to form the pasta strands. Drape the freshly cut tagliatelle over your hand and transfer it to a floured surface or baking sheet to dry for about 30 minutes. Alternatively, use a pasta drying rack for this step.

To Make Without a Pasta Maker:

• Take a small portion of dough and roll it out on a floured surface into a rectangle, approximately 6 inches (15 cm) by 12 inches (30 cm). Roll the dough loosely into a flat cylinder, starting from the edge closest to you.
• Using a sharp knife, slice the rolled dough into strips of your desired width, such as 3/16 inch (5 mm). These slices will determine the thickness of your tagliatelle. Unroll the strands and lay them on a floured surface or drying rack.

Cooking and Storing the Pasta:

• Fresh pasta is best cooked immediately. If you plan to store it, divide the pasta into portions, place each in a freezer bag, and freeze for up to three months. When needed, boil the frozen pasta directly in water without thawing, cooking for a few minutes until it floats.