Finely chop the shallots and garlic. Have the rest of the ingredients ready to go.
Season the chicken breasts with salt and pepper on both sides.
Pre-heat your saute pan (frying pan) until drops of water quickly evaporate. This means the pan is at least 212° F.
Heat butter and oil in a heavy bottomed pan over high heat until butter stops foaming and just starts to turn a light brown.
Sauté the breasts until they are lightly browned on one side, approx. 3 minutes.
Turn breasts over and sauté for another 3 minutes, again until lightly browned. (At this point the meat should be firm to the touch.)
Transfer the chicken breasts to a plate, cover with aluminum foil, and keep warm in the oven or toaster oven set at low.
Remove the pan from the head source, and add half of the wine to deglaze the pan, stirring to dissolve the flavorful brown particles stuck to the pan.
Return pan to the stove and add the shallots and cook until translucent, about 2 minutes.
Add the garlic and cook for 1 minute, making sure the garlic doesn’t burn. (It makes the dish bitter if it does)
Add the remaining wine and reduce (boil) until only a trace of wine is left in the pan.
Add the chicken stock and reduce to half the original amount, approx. 6-7 minutes.
Add the cream, and again reduce until the sauce is thick enough to coat a spoon.
Spoon sauce over cutlets and serve.