Remove any excess fat from the chicken breasts, but keep the skin intact. Consider using airline cut chicken breasts (where the wing bones are still connected but clean of any meat). This makes for a nice presentation.
Season the breasts on both sides with salt and pepper. Place the chicken into your bag(s).
Add 1 oz of oil, sliced mushrooms, rosemary, and stock to the bag. Seal the bag, and sous vide at 154° F for 1 hour.
45 minutes into the sous vide cook, start the marsala wine sauce. Add 1/2 ounce olive oil into a small sauce pan. Add the diced shallots and garlic to the pan and begin to sweat on low heat until translucent and soft.
Increase the heat slightly to your saucepan to add the marsala wine. Simmer until the wine volume is reduced in half. Remove the pan from the heat until the chicken has finished the sous vide cook.
Open the bag and remove the chicken breast and toss the herbs, reserving the liquid and mushrooms. Place your saucepan back onto the heat and add the liquid and mushrooms from the bag. On medium to high heat continue to reduce the contents of the pan while you complete the next step. Stir frequently so it won't burn.
Heat a cast iron skillet to the point that the metal on its own begins to release light smoke. Then add the remaining olive oil. Wait for the oil to reach it's smoke point. Lightly season your chicken breasts again, then place them skin side down into the pan for about 45 seconds to 1 minute. Flip and repeat.
Pro tip: Add a few tablespoons of butter to the pan and using a spoon carefully ladle the brown butter over the chicken to impart more flavor.
Place the fully seared breasts on a serving plate.
Use a whisk to combine the water and cornstarch together. Make sure your saucepan contents are near-boil and slowly whisk the cornstarch slurry into the pan until you achieve the proper consistency. The sauce should coat the bottom of a spoon evenly - this is "au sec" in French cooking. When wiped with your finger it should leave a clean streak. Season the sauce to taste with salt and pepper, then ladle the it over the chicken and plate.