Heat a large frying pan over medium heat. Drizzle the olive oil into the pan. Add the chicken and sprinkle with the ½ teaspoon salt. Cook for about 7 minutes until the bottoms are golden. Flip. Cook until the chicken reaches 155 with a meat thermometer.
Meanwhile, whisk together the melted butter, softened cream cheese, white wine (if using), mustard, lemon juice, and salt. Whisk until a thick sauce forms.
Top the cooked chicken with the sauce. Sprinkle on the ham and cheese on top of the sauce. Cover with a lid and cook until the cheese is melted and the chicken is 160 degrees when checked with a meat thermometer.
Alternatively, broil for 2-3 minutes after topping until the cheese is melted and golden.
To Reheat: place on a microwave-safe plate and heat up for 1 or 2 minutes until it's hot. Or you can reheat in a casserole dish in the oven at 350 degrees for 10-12 minutes. To Freeze: put in a food container that has a sealed lid. Store in the freezer for up to 1 month. It's best to thaw in the fridge overnight before reheating. Substitutions: swap the swiss cheese for any white-colored melting cheese like mozzarella or provolone.