Preheat the oven to 400℉.
Heat the olive oil and butter in a large oven-safe skillet over medium heat. Add the shallots and garlic, season lightly with salt and black pepper, and cook for 2 to 3 minutes until softened.
Add the cubed chicken and cook for another 2 to 3 minutes, stirring occasionally, until lightly colored. Stir in the diced ham, then pour in the chicken stock and bring to a boil.
Add the pasta, reduce heat to a steady simmer, cover, and cook for 10 to 12 minutes, stirring occasionally, until the pasta is al dente.
Uncover and stir in the heavy cream. Taste and adjust seasoning as needed. Stir in half of the Swiss cheese until melted.
Sprinkle the remaining Swiss cheese and panko breadcrumbs evenly over the top.
Transfer to the oven and bake for 8 to 10 minutes, until the cheese is melted and the top is lightly golden. Remove from the oven and garnish with fresh parsley before serving.