Creamy Champagne Chicken

Name: Creamy Champagne Chicken
Prep time: 5 min
Cook time: 25 min
Total time: 30 min
Cuisine: American, French
Ingredients: 1 tablespoon olive oil; 2 skinless boneless chicken breast fillets (halved horizontally to make four fillets); 1 pinch salt (to season); 14 ounces mushrooms (sliced); 2 teaspoons butter; 1 french shallot (large, finely chopped - normal shallot for U.S readers); 1/2 cup champagne (or sparkling white wine); 2/3 cup milk (or heavy / thickened cream); 1 teaspoon cornstarch (corn flour - only if using milk); 1 pinch fresh parsley (to garnish)