Bring a large pot of salted water to a rolling boil and cook the bucatini until al dente according to package directions.
While the pasta cooks, whisk the eggs in a bowl until smooth, then stir in the chopped parsley, chopped basil, and grated Parmesan; season with a pinch of salt and pepper.
When the pasta is done, reserve a small cup of pasta cooking water, then drain the pasta and return the hot pasta to the empty pot off the heat.
Working quickly, pour the egg, herb, and cheese mixture over the hot pasta and toss continuously with tongs or a fork so the residual heat gently cooks the eggs and forms a creamy sauce; add a splash of reserved pasta water if needed to loosen the sauce.
Add the butter and toss until melted and evenly coating the pasta; taste and adjust seasoning with more salt and pepper if desired.
Serve immediately while creamy and hot.
