Preheat oven to 350 degrees.
Heat a cast iron skillet with a thin layer of olive oil on high to medium high.
Sear chicken thighs, skin sides down, for approximately 3 minutes. Be careful as splattering can occur.
Turn chicken over and sear the bottoms for about 2 minutes.
Lower skillet heat to medium or medium low, then carefully remove chicken thighs and set aside on a plate.
Add about ¼ cup of marsala wine to the skillet to deglaze the pan.
Place potatoes and mushrooms into the pan and move around to coat.
Sprinkle hefty pinches of kosher salt over potatoes and mushrooms, as well as several grinds of peppercorn.
Let potatoes and mushrooms cook for approximately 4 minutes, moving around in skillet frequently.
Add chopped garlic to skillet and mix in and stir for approximately 1 minute.
Then add ¼ cup more marsala to pan and stir around.
Let simmer for approximately 3 minutes, or until a bit of wine has been reduced.
Then add ⅓ cup of heavy cream to the skillet and stir to mix well.
Add another ¼ cup of marsala and mix well, coating potatoes and mushrooms.
Place chicken thighs back into pan and push aside mushrooms and potatoes, so they are not underneath the chicken pieces.
Sprinkle everything with salt and pepper then place skillet into hot oven.
Let cook for approximately 20 minutes, then add ⅓ cup more heavy cream to sauce.
Evenly stir cream into sauce throughout pan until mixed well. You will be moving around the food slightly.
Sprinkle basil all over sauce in dish and mix in.
Continue cooking for another 25 minutes or until chicken is cooked thoroughly and no longer pink inside.
Note: Oven temps and times may vary, as well as stove tops.