Add a drizzle of olive oil to a pan heated on medium. Thoroughly cook the chicken breast. Timing depends on how thick the chicken breast is. Once the chicken is done cooking, set aside on a cutting board.
Now to make the sauce, in a large pot melt down the stick of butter on medium-low heat. You'll want it to melt slowly. At the same time, add in the 1/2 cup of milk or heavy cream. Ensure that you do not reach a boil, you just want it to get some heat.
Bring a large pot of water to a boil, and make sure to salt the water. I like to use sea salt. Once boiling, add in the pasta and cook as per box instructions.
Once the butter is completely melted, add in the parmigiano cheese or pecorino cheese. Stir to thicken the alfredo sauce. Now add in black pepper, personal preference, add as much as you'd like.
Cut the chicken breast into your desired size, I personally like to cut it into strips.
Once the pasta is done, strain the water, and dump the pasta into the alfredo sauce and mix well. The sauce will thicken more, and coat the pasta.
Serve on a plate, and place desired chicken breast pieces on top. Finish off with more black pepper, parsley, and cheese.