Heat 1 tsp of the butter in a pot or a large skillet over high-medium heat
Add salt and pepper to the chicken and put the chicken into the pot
Cook for around 5-7 minutes until slightly brown and cooked through
Remove the meat from the pot.
Add the second tsp of butter and the garlic and cook for 1-2 minutes
Pour in the chicken stock and milk, add the mustard and the nutmeg, stir and bring to boil.
Once boiling add the pasta and give it a good stir.
Reduce heat to medium-low and cook pasta for 9-10 minutes while stirring regularly (note 1)
Once the pasta is cooked, remove the pot from the stove, add all three cheeses and stir thoroughly to bring them all to melt.
Add salt and pepper to taste.
Put the chicken with all the accumulated juices into the pot, fold it in and serve immediately.
Cooked in fluids like milk, pasta needs about 2 minutes longer than the cooking time written on the package. But since it will keep on cooking in the sauce take it from the stove when it's still a bit firm.
Use a dutch oven or heavy bottomed pan to make this recipe. They will distribute the heat more evenly and you will be less likely to scorch the milk.
Taste the pasta and sauce before adding the chicken and adjust the seasoning as needed.