In a large bowl, whisk together the gluten-free flour blend, xanthan gum (if using), and salt.
Make a well in the center of the flour mixture and add the eggs and olive oil.
Using a fork, beat the eggs and oil together, gradually incorporating the flour from the sides of the well.
Once the dough starts to come together, use your hands to knead it until it forms a smooth, pliable ball. If the dough feels too dry, add water, 1 teaspoon at a time, until the desired consistency is reached.
Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes.
Divide the dough into four equal portions. Work with one portion at a time, keeping the others covered to prevent drying.
On a lightly floured surface (use gluten-free flour), roll out the dough portion until it's about 1/8-inch thick. You can also use a pasta machine, following the manufacturer's instructions for gluten-free dough.
Cut the pasta into your desired shape using a sharp knife or pasta cutter. You can make fettuccine, lasagna sheets, or any other shape you prefer.
Repeat the rolling and cutting process with the remaining dough portions.
Bring a large pot of salted water to a boil. Add the fresh pasta and cook for 3-5 minutes, or until it reaches your desired tenderness.
Drain the pasta and serve it with your favorite gluten-free sauce.