Add cheeses, parsley, salt, pepper, and garlic olive oil to eggs. Stir to mix.
Boil 2 quarts water with 1½ tsp salt. Add pasta. Cook until al dente. RESERVE ½ CUP PASTA WATER. Drain pasta and return to cooking pot.
Add egg/cheese mixture to hot pasta along with 1 tbsp pasta cooking water. Stir vigorously until cheese is melted and sauce is smooth. Add additional cooking water if needed.