In a large bowl, combine the all-purpose flour and kosher salt. Make a well in the center.
Beat the eggs with olive oil in a small bowl. Slowly pour the egg mixture into the well, gradually mixing with the flour. If the mixture is too dry, add 1 teaspoon of water at a time until a soft dough ball forms.
Turn the mixture out onto a lightly floured surface and knead for about 4 to 8 minutes until the dough is smooth and elastic.
Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes.
Divide the dough into four equal parts. Roll each piece out with a rolling pin until about 1/8-inch thick. Cut the rolled dough into 12-inch long strips.
Bring a large pot of salted water to a boil. Add a few noodles at a time and cook for 1 minute until just tender. Drain and lay them on a lightly floured surface until ready for use in your lasagna.