Place the flour in a large mixing bowl and make a well in the center.
Crack the 6 eggs into a small bowl, then add them to the well in the flour.
Use a fork to gradually incorporate the flour into the eggs until a dough forms, then knead with your hands until smooth; add a little water if the dough is too dry to come together.
Form the dough into a ball, dust it with flour, cover with a damp towel, and let it rest until slightly relaxed, about 20–30 minutes.
Preheat the oven to 350°F (175°C).
Cut the dough into 4 equal pieces. Work with one piece at a time and keep the remaining pieces covered.
Roll one piece very thin with a rolling pin until nearly paper thin, dusting with extra flour as needed to prevent sticking.
Transfer the rolled sheet to a baking sheet and place in the oven for a few minutes to dry slightly; it should be dry to the touch but still pliable and not cracking.
Move the sheet to a cutting surface and cut the sheet into long rectangles about 3 inches wide (or wider if preferred), stack the rectangles, and cut very thinly across the width to form angel hair strands.
Spread the cut noodles on a flat surface or tray to dry completely; they should not be wet before storing.
Repeat rolling, drying briefly in the oven, and cutting with the remaining dough pieces.
To cook, bring a large pot of water to a boil with salt and a splash of olive oil, add the pasta, and cook about 2 minutes until tender; drain and toss with a little olive oil to prevent sticking.
Once completely dry for storage, transfer pasta to a paper box or dry container and keep in a dry place.
