Bring a large pot of well-salted water to a boil and cook pasta to al dente according to directions on box. (I usually undercook the pasta by about a minute.)
Wipe out the skillet from the pangritata, add olive oil and butter. Melt together over medium heat.
Add the garlic and crushed red pepper and immediately break the eggs into the skillet.
If need be, lower the heat a bit. You want the garlic to cook without burning and the egg whites to set, but the yolks to remain runny. *Note - you can accomplish the same thing by separating the egg whites and yolks. Add the whites in first and the yolks later.
Drain the pasta well, reserving 1 c of the cooking liquid.
Add pasta back to the pot,
pour the eggs and all the fat from the skillet over the pasta.
add the parsley and toss well, breaking up the eggs as you do.
If you prefer a wetter dish, you can add in some of the reserved cooking liquid.
Plate the pasta and eggs, season well with freshly ground black pepper,
sprinkle with the grated cheese and then top with the pangritata.