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 gently to close.
In a small saucepan, boil the chicken stock and cream 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.
In a shallow bowl, beat the eggs. Beat 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 the chicken for about 12 minutes, until just cooked through. Reheat the mustard sauce and pour onto plates. Set the cutlets on the sauce and serve.
