Preheat the oven to 350°. Using a small knife, cut a 4-by-3-inch pocket in the side of each chicken cutlet. Insert a havarti slice and spread 1 teaspoon of thyme in each pocket; press closed.

In a shallow bowl, beat the eggs and add in the Parmigiano-Reggiano. Put the flour in another shallow bowl.

In a large nonstick skillet, heat 1/4 inch of olive oil. Season the cutlets with salt and pepper. Dredge 2 cutlets in flour, shaking off the excess, then coat with the beaten egg. Fry over moderately high heat until golden, about 2 minutes per side. Transfer to a large rimmed baking sheet. Coat and fry the remaining cutlets.

Bake chicken for about 12 minutes, until just cooked through.

While the chicken is in the oven, boil the chicken stock and cream in a small saucepan over moderately high heat until reduced to 1/2 cup, about 5 minutes. Whisk in the mustard and boil for 30 seconds, whisking a few times. Season with salt and pepper and remove from the heat. Pour onto plates. Set the cutlets on the sauce and serve, topping with additional sauce if desired.