Cut chicken thighs/ fillets into chunks, chop carrot and onion.
Grind the chicken pieces , carrot, onion and garlic in a food processor with the meat grinder attachment. If you don't have a meat grinder, use a sharp knife to chop the chicken, grate carrot, chop onion and mince garlic.
Season the mixture with salt and black pepper. Add egg and milk and mix well.
Preheat the oven to 400 F/ 205 C.
Add 1 tbsp. of melted butter to the iron skillet.
Using a meat baller/ice cream scoop, form about 15-20 balls. I recommend to use a meat baller or an ice scream scoop because meatballs will have the same size and be cooked more evenly.
Transfer the meatballs to the baking skillet and bake 25-30 minutes.
In the meantime, heat cream and water in a small saucepan. Once the cream is hot, add the grated cheeses and stir in Dijon mustard. Season with salt, nutmeg and pepper, add rosemary springs. Cook 1-2 minutes or until cheeses are melted.
Once meatballs are cooked, remove from the oven and pour the creamy cheesy sauce over them.
Serve with mashed potatoes or noodles.