Mix the flours and salt in a large bowl and make a well in the centre. Add the olive oil, egg and water. Combine ingredients by hand until a shaggy dough forms.
Turn dough onto work surface. Knead for 10 minutes, adding more flour to keep dough from sticking, until it is smooth, elastic, and doesn't easily tear when you pull it apart.
Wrap dough tightly with plastic wrap and let it rest for at least an hour, giving the gluten time to relax. When the hour is almost up, set a large pot of salted water on the stove to boil.
Once dough is rested unwrap it. On a clean wood or stainless steel surface pat dough into a rectangle. Using a knife or dough cutter, slice off a thin piece of dough, keeping the remaining dough covered with a damp towel.
Begin to roll out the dough with your fingers, starting in the middle and working towards the outside. The noodles should be about the thickness of a pencil.
Place rolled noodles lengthwise on a floured tray to avoid sticking. Continue until all the dough has been made into pici pasta.
Bring 3 quarts water to a boil in a 5-qt. pot. Season with salt; add pici pasta and cook for 4-5 minutes, stirring occasionally, until about 2 minutes before tender. Drain, reserving 3/4 cup pasta cooking water.
Meanwhile, melt 2 tbsp butter in a large skillet over medium heat. Add pepper and cook, swirling pan, until toasted, about 1 minute.
Add 1/2 cup reserved pasta water to skillet and bring to a simmer. Add pasta and remaining butter. Reduce heat to low and add Parmesan, stirring and tossing with tongs until melted. Remove pan from heat and add Pecorino, stirring and tossing until cheese melts, sauce coats the pasta, and pasta is al dente.
Transfer Cacio e Pepe Pici Pasta to bowls and serve with freshly cracked pepper and grated Pecorino cheese.