Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente; drain and set aside.
Heat a skillet over medium heat and add the olive oil and butter until the butter melts.
Add the minced garlic and sauté 30–60 seconds until fragrant and just beginning to turn golden—do not burn.
Pour in the chicken broth and heavy cream, stir to combine, then season with salt and black pepper; bring to a gentle simmer.
Reduce heat and simmer a few minutes to slightly thicken the sauce.
Add the drained fettuccine to the skillet and toss until evenly coated in the sauce.
Stir in the Parmesan and chopped parsley until the cheese melts and the sauce is creamy.
Serve immediately with lemon wedges to squeeze over the pasta as desired.