Sprinkle the fillets on all sides with salt and plenty of pepper.
Melt the butter in a heavy saucepan. Add the onion, carrots and garlic and cook about 10 minutes but don't brown them. Sprinkle over the flour and stir to blend. Arrange the fillets in a single layer and sprinkle with thyme, bay leaf, parsley and celery. Cover and let cook 5 minutes. Add the vermouth, cream and stock, cover and simmer 20 more minutes.
Remove the chicken to a plate and keep warm. Pour the sauce into a blender and blend until smooth. Return to the saucepan and add more salt if needed. Add the mustard, stir and remove from the heat. Pour the sauce over the chicken and serve!