Be sure to knead this dough thoroughly or your pasta will turn out too soft. Resist the urge to salt the dough; it will inhibit gluten development. Instead, season the pasta water heavily—it should taste like the sea.
If using a stand mixer: Combine 00 flour and semolina flour in the bowl of a stand mixer fitted with the dough hook attachment. With mixer running on low speed, gradually add beaten egg, using only enough to form a stiff dough. (You may not need all of the egg.) Turn dough out onto a clean surface, and proceed to step 2. If using a whisk and fork: Whisk together 00 flour and semolina flour in a large bowl, and transfer to a large, clean work surface. Make a well about 4 inches in diameter in center of flour mixture. Gradually pour a small amount of beaten egg into well, stopping occasionally and using a fork to incorporate by pushing some of the flour mixture from inside edge of well into egg. Continue adding beaten egg, and incorporating all flour mixture until a shaggy dough forms. (You may not need all of the egg.) Proceed to step 2.
Knead dough until smooth and elastic, about 10 minutes. Shape into a ball, wrap tightly in plastic wrap, and chill at least 1 hour or up to 4 hours.
Divide dough into 4 portions. Working with 1 dough portion at a time (keep remaining portions covered with a towel), flatten dough to 1/3-inch thickness. Roll flattened dough through pasta machine with rollers on widest setting. Fold dough in half crosswise, and reroll through pasta machine until dough is as wide as the pasta machine (about 5 inches). Continue rolling dough through pasta machine, reducing width of rollers one setting at a time, until dough has been rolled through setting 4 (about 1/10-inch thickness), flouring dough with 00 flour as needed to prevent sticking.
Flour both sides of dough, and fold in half crosswise. Repeat folding in half 2 more times to form 8 layers. Cut dough crosswise into 1/8-inch-wide pieces. Unfold pasta, sprinkle with 00 flour, and cut in half, crosswise, to form pieces about 15 inches long. Transfer pasta to a rimmed baking sheet dusted with semolina flour, and cover with plastic wrap. Repeat with remaining dough. Pasta can be covered and refrigerated up to 1 day or frozen in ziplock plastic freezer bags up to 3 weeks.