Cut chicken breast into two halves lengthwise. Use a meat mallet/rolling pin to pound the chicken on the thick parts, so that it is of even thickness and cooks evenly.
To dredge the chicken, mix together flour, parmesan, Italian seasoning, salt and pepper. Coat chicken breast well with the mixture by pressing it into the flour mixture and shake off any excess flour.
Heat olive oil in a pan. Swirl the pan to evenly distribute oil. Working in batches, add the chicken cutlets to the pan(don't overcook).
Cook chicken breast 3-4 minutes on each side. The crust should look crisp and golden brown. Keep aside the cooked chicken breast covered.
Clean the pan if you see burnt bits of residual flour from frying the chicken . Melt butter.
When the butter is just hot enough, add garlic and thyme sprig. Saute on low heat for a minute until it is aromatic.
Lower the heat, slowly add chicken stock, heavy cream, salt, and pepper. Deglaze the pan scraping any bits stuck to the bottom of the pan. Gently simmer it for about 30 seconds.
Add fresh lemon juice to the sauce and allow the sauce to gently simmer for a couple of minutes. The sauce will start to thicken.
Switch off the flame, add the chicken back to the pan, and pour over the sauce.
Sprinkle fresh parsley on top and serve.