While you wait for water to boil, mince the garlic cloves finely, dice the onion into small pieces, and slice the mushrooms into 1/4-inch thick slices. Season the chicken breast pieces with 1/2 teaspoon of salt and 1/4 teaspoon of pepper on all sides. Bring a large pot of salted water to a rolling boil and add the fettuccine, cooking according to package directions until al dente. Once the pasta reaches the desired texture, drain it in a colander and set aside—don't rinse it, as the starch helps the sauce cling better.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until shimmering. Working in two batches if needed to avoid overcrowding, add the seasoned chicken pieces and cook for 5-6 minutes, stirring occasionally, until they develop a golden-brown color on the outside and reach an internal temperature of 165°F. Transfer the cooked chicken to a plate and set aside.
Add the butter to the same skillet with the remaining oil (no need to clean it—those browned bits add tremendous flavor). Add the diced onion and sauté for 3 minutes until softened and translucent. Add the sliced mushrooms and cook for 6-7 minutes, stirring occasionally, until they release their moisture and begin to brown—I find mushrooms cooked this way develop a much richer, deeper flavor. Stir in the minced garlic and cook for just 30 seconds until fragrant, being careful not to burn it.
Pour the 4 cups of half and half into the skillet with the aromatics and mushrooms, stirring to combine. Reduce the heat to medium-low and simmer gently for 8-10 minutes, stirring occasionally, until the sauce reduces slightly and thickens—you should see it coat the back of a spoon. Avoid boiling aggressively, as the half and half can separate if the temperature gets too high.
Return the cooked chicken from Step 2 to the skillet and stir well. Remove from heat and immediately stir in the 1/2 cup of grated Parmesan cheese, 1/4 cup of fresh parsley, and the remaining 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Add the drained fettuccine from Step 1 and gently toss everything together until the pasta is evenly coated with the creamy sauce. Let the dish rest off heat for 1-2 minutes to allow the flavors to meld.
Divide the chicken fettuccine alfredo among serving bowls or plates immediately while it's warm and creamy. I recommend adding an extra sprinkle of fresh Parmesan and a few turns of fresh cracked pepper on top of each serving for both visual appeal and extra flavor.