Fill a large pot with lightly salted water and bring to a rolling boil. Cook fettuccine at a boil until tender yet firm to the bite, about 8 minutes. Drain and toss with 1 tablespoon olive oil. Set aside and keep warm.

Heat remaining tablespoon olive oil and butter in a skillet over medium heat. Add chicken and leeks; cook and stir until leeks are tender and chicken is no longer pink in the center and juices run clear, 5 to 7 minutes. Add garlic; cook and stir until fragrant, 1 to 2 minutes. Pour in chicken broth; continue cooking 2 to 3 minutes more. Pour in heavy cream. Reduce heat; let simmer until thickened, about 5 minutes.

Stir Gorgonzola cheese and walnuts into the skillet with the chicken; continue to simmer until cheese has melted, 2 to 3 minutes. Season with salt and pepper. Toss with cooked pasta. Top with parsley.