Grease a baking dish with fat. Cut each of the 8 chicken breast fillets in half to make 16 halves. Wrap each half in a ham slice. Refrigerate until ready to bake.
Place the wrapped chicken halves side by side in the greased baking dish.
Pour roughly 1 cup of milk into a saucepan and heat over medium-high heat until it comes to a boil, about 5 minutes. Remove from heat and add the 2 packs of cream cheese and herbs. Stir constantly until the cheese is completely dissolved, about 1-2 minutes. While the sauce is still hot, sprinkle flour into the saucepan a little at a time, stirring constantly, until the sauce thickens to a medium consistency. Remove from heat and stir in the 1 cup cream. Season with lots of dill and grated cheese to taste.
Pour the cheese sauce over the chicken in the baking dish and sprinkle more grated cheese on top.
Bake in a preheated oven at 200 °C (392 °F) for 40-45 minutes, until the chicken reaches an internal temperature of 74 °C (165 °F).
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