Slice chicken breast in half lengthwise, season each piece with salt and pepper and dredge in flour.
Heat up 1 tablespoon of oil in skillet with 1 tablespoon of butter. Cook chicken until golden brown, about 4 to 5 minutes per side. The internal temperature should register 165 degrees F. Remove onto a plate.
To the same pan, add more oil. Add minced garlic and shallot and saute until soft and fragrant. Add lemon zest, lemon juice and chicken stock. Scrape the bottom of the pan with a wooden spoon so all of the browned bits from cooking chicken are mixed into the sauce. Simmer for 2 minutes.
Add heavy cream, stir and return chicken to pan. Let everything heat up. Turn the heat off. Add remaining tablespoon of butter and let melt in the hot sauce. Garnish with chopped parsley and serve.
For a lighter sauce, you can use half and half or a mixture of milk and cornstarch so it will still thicken to a sauce consistency. For that, use 1 and 1/2 teaspoon of cornstarch and 1/2 cup of milk.
Please note, that the nutrition value can vary depending on what product you use. The information below is an estimate.