Bring a large pot of salted water to a boil and cook the fettuccine according to package instructions until al dente; drain and set aside.
Meanwhile, heat the olive oil and butter in a skillet over medium heat until the butter melts.
Add the minced garlic and sauté until fragrant and just beginning to brown, about 30–60 seconds.
Pour in the chicken broth and heavy cream, stir to combine, and season with salt and black pepper.
Lower the heat and simmer the sauce briefly until it reduces slightly and thickens, about 2–3 minutes.
Add the drained fettuccine to the skillet and toss to coat evenly with the sauce.
Remove from heat, stir in the Parmesan and chopped parsley, then taste and adjust seasoning if needed.
Serve immediately with lemon wedges for squeezing over each portion.