Heat the oil in a large skillet, saucepan or casserole over a high heat. Season the chicken breasts generously with salt and pepper. Place the chicken breasts in the pan and cook for 3 to 5 minutes, or until they are golden and caramelised, before turning them over and cooking them for another 3 to 5 minutes. The best way to achieve a nice colour on the chicken is to not move the chicken too often.
Once the chicken breasts are golden and caramelised on both sides, remove them to a plate. The chicken does not need to be fully cooked through at this stage.
Add a bit more oil to the pan as needed, then add the shallots (or onions) and garlic. Cook on a medium heat for 3 to 4 minutes until they have softened.
Pour the white wine into the pan and let it simmer for 2 to 3 minutes until it has reduced slightly. Use a wooden spoon to stir the mixture and to lift any caramelised bits from the pan.
Pour in the chicken stock and cream, together with the fresh tarragon. Let the sauce simmer gently for 4 to 5 minutes.
Taste to check the seasoning and add more salt and pepper, as needed.
Slowly pour in the cornflour slurry, stirring the sauce as you do. You may not need all of the cornflour and water mixture – use as much as you need until the sauce has thickened slightly.
Return the chicken to the pan, turn the heat down to medium low, and cover with a lid. Cook gently for 5 to 10 minutes, or until the chicken pieces have cooked through (I use a Thermapen to check they’re cooked to 74C).
Garnish with parsley or more tarragon before serving. It’s delicious with roast potatoes or mashed potatoes, plus your favourite veg. It’s also delicious with pasta (see Notes).