Start by warming the olive oil in a large pan over medium-high heat, creating a lovely base for your chicken to sear beautifully.

Season the chicken breast fillets with salt, then carefully place them in the pan. Sear until they're golden brown on both sides and cooked through, about 6-7 minutes per side. Remove and let them rest.

In the same pan, add the butter and toss in the mushrooms. Sauté them for about 5 minutes until they’re tender and wonderfully fragrant.

Add the chopped French shallot to the mushrooms and cook, stirring often, until they become translucent, which should take about 2-3 minutes.

Pour in the champagne or sparkling white wine. Scrape any bits from the bottom of the pan and let it simmer for 2-3 minutes to reduce and intensify the flavors.

Stir in the milk or heavy cream, bringing the mixture to a gentle simmer. You'll want to see small bubbles forming but not a rolling boil, for about 3-5 minutes.

Mix the cornstarch with a splash of water to make a slurry. Add this to your sauce while stirring, allowing it to thicken and take on a luscious consistency, about 2 minutes.

Return the seared chicken to the pan, ensuring it gets beautifully coated in that creamy sauce. Let it heat back up for another minute or two.

Finally, sprinkle with finely chopped fresh parsley before serving, adding a touch of color and freshness that enhances the dish.