Begin by seasoning the chicken breast on both sides with salt and pepper.
In a large skillet, warm the olive oil over medium-high heat and add the seasoned chicken, cooking it for about 2 minutes per side until golden and cooked through. Transfer the cooked chicken to a plate to rest for 5 minutes, then slice it thinly while the pasta cooks.
In the same skillet, combine the milk, chicken broth, and minced garlic. Bring this to a gentle simmer before adding the fettuccine.
Stir the pasta every 30 seconds to avoid sticking and to allow it to soften, which should take approximately 3 minutes. When softened, lower the heat to medium and stir every few minutes.
After about 9-10 minutes, the pasta should be nearly finished, still retaining some liquid in the skillet. At this point, mix in the heavy cream and grated parmesan cheese.
Allow the mixture to simmer while stirring occasionally for about 2 minutes, until the sauce has thickened and the pasta is fully cooked. To adjust the consistency, add a splash of hot water if it becomes too thick.
Taste the dish and season with additional salt and pepper as preferred, then serve right away with a sprinkle of freshly grated parmesan and garnished with parsley for an inviting presentation!