Pat the chicken breast dry using paper towels and sprinkle both sides of the breasts with salt and pepper.
Heat a Dutch oven over medium heat and add the oil. When the oil shimmers, add the butter and the chicken breasts. Cook the chicken breasts 3 minutes or until the pan-side is golden brown. Flip the breasts over and cook another 2-3 minutes. Transfer the breasts to a plate; set aside.
Add the carrots and celery to the still-hot Dutch oven and, if needed, add 1-2 more tablespoons oil. Cook the vegetables 3 minutes, stirring occasionally. Add the onions and cook another 3 minutes or until the onion has softened and is translucent.
Slowly add the chicken stock, while stirring to deglaze the pan, and add the wine. Stir well. Bring the stock to a boil.
Add the thyme, nutmeg, mustard and pasta. Stir well and bring back to a boil. Reduce the heat to medium-low and simmer the soup about 30 minutes. The pasta should be cooked through and the broth thickened.
While the soup simmers, cut or shred the cooked chicken breasts.
After 30 minutes, turn the heat to medium and add the milk and cut chicken breasts.
Bring the soup just to a boil and immediately reduce the heat to low. Cook the soup 10 minutes or until it has thickened slightly.
When it is the desired consistency (soup-ish but not stew-ish), add the cheeses and stir until cheese has melted.
Season to taste with salt and pepper.
Ladle the soup into bowls and top with one or two Toasted Cheesy Crostini (depending on the size).
Garnish with chopped fresh parsley, sprinkle lightly with smoked paprika or grated nutmeg and…