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.
While the pasta cooks, heat the olive oil and butter in a large skillet over medium heat until the butter is melted.
Add the minced garlic to the skillet and sauté until fragrant and just beginning to color, about 30–60 seconds.
Pour in the chicken broth and heavy whipping cream, stir to combine, and season with the salt and ground black pepper.
Lower the heat and simmer the sauce briefly until it reduces and thickens slightly, about 2–3 minutes.
Add the drained fettuccine to the skillet and toss to coat evenly with the sauce.
Remove from heat, sprinkle with chopped parsley and shredded Parmesan, then toss gently. Serve with lemon wedges to squeeze over each portion.
