Boil the pasta according to package instructions. Before draining it, reserve 1/4 cup of the starchy water and set it aside.

Heat the olive oil in a large pan over medium to medium-high heat. Place the chicken breast in the oil and brown it on one side for four to five minutes or until golden brown. Flip it over and cook it on the other side until browned and the internal temperature is 165°F. 

Remove the chicken from the pan and set it aside on a cutting board. Adjust the heat to medium, add the diced ham to the same pan, and cook it for a couple of minutes. While it cooks, cut the chicken into bite-sized pieces.

Add the butter to the pan with the ham. Stir, and once the butter is melted, add the flour, salt, and pepper. Stir and cook the mixture for a minute.

Add the milk to the pan while whisking to create the sauce. Whisk until there are no lumps of flour. Once the milk is steaming hot (not boiling), add the shredded cheese and stir until it melts into the sauce.

Add the cooked chicken and pasta to the pan and stir to combine. Add a splash or two of the reserved pasta water and stir again. Garnish with parsley if using.