Add oil and onion and cook over medium heat until softened.
Remove from heat, add chicken broth, salt and butter.
Bring a pot of salted water to a boil.
Add fettuccine.
Add eggs in their shells to pasta pot and cook until pasta is al dente. Reserve 1 cup pasta cooking water and drain pasta and eggs in a colander together.
Bring sauce in skillet to a simmer.
Add pasta and cook, stirring until heated through.
Transfer pasta to a large bowl, add 1/2 to 1 cup cooking water and 1/4 cup Parmesan cheese and toss well. Peel eggs and chop.
Sprinkle egg, crumbled bacon and chives on pasta and toss. Season with pepper and toss again.
Sprinkle remaining 1/4 cup cheese over individual servings.