If you are using an 8-inch wheel of brie, slice it into quarters. Save one quarter for snacking! Slice the other three quarters into 1/4-inch slices. Place on a plate and pop in the freeze while you prep the chicken.
Lay each chicken down horizontally with the tip of the breast pointing to your right. Use a pairing knife to gently cut a slit in the top of the breast, this will be to your left. Use your knife to make a pocket in the breast but do not cut through to edges. After you have finished making a pocket for the brie in each chicken breast, place each breast between two pieces of plastic. Pound it out ever so slightly so the breasts are even in thickness. Don't pound too hard or make them too thin or the chicken will tear.
Stuff the brie slices in the chicken pockets. Season the chicken with salt and pepper. I find you don't need to seal them with toothpicks because while the chicken is cooking the brie oozes out and creates the most delicious sauce!
Heat a large cast iron skillet to a medium-high heat. Add one tablespoon of butter and one tablespoon olive oil or avocado oil. When the oil is very hot, add the chicken. Sear the chicken until golden brown, flip over and sear on the other side. It should take 3-4 minutes per side. You may have to cook the chicken in batches. If you do, you will need to add one more tablespoon of butter and olive oil for the second batch.
Remove the seared chicken to a plate. Add another teaspoon of butter and olive oil. Add the peaches. Cook the peaches on medium high until slightly brown. Add the corn. Cook another minutes.
Remove the pan from the heat. Add 1/4 cup of the brandy. Use a wooden spoon to scrape up all the brown bits. Pour in the chicken broth. Bring to a boil and reduce to a simmer.
Add the chicken back to the pan. Cover with a lid and continue to simmer until the chicken is cooked through. Another 7-8 minutes. It should reach 165 degrees on a meat thermometer. The brie WILL run out of the chicken and that's okay! It will make the sauce thick and tangy and delicious! If you want, you can use a spoon to scoop some of the brie back into the kitchen.
When the chicken is cooked through, remove the lid. Season the sauce with salt and pepper. Garnish with plenty of fresh basil.