Begin by placing the chicken breasts between two layers of plastic wrap on a large cutting board (or place them in large ziploc bags).Using the flat side of a meat mallet, pound out the chicken breasts until they are only about 1/3"-1/2" thick. Try to make them as uniform as possible. Remove plastic and season with 1/2 teaspoon of salt, evenly distributing across the chicken.
Heat a large skillet over medium-high heat. Once hot, add oil to pan.
Using tongs, place chicken pieces in pan. You will have to cook these in batches - so don't crowd the pan. Cook about 3-4 at a time depending on size.
Sear the chicken on each side for 4-5 minutes, until golden brown. Once browned, cover the pan for 2-3 minutes to finish cooking through. You can test to see if the chicken is cooked through by using a meat thermometer (chicken is done at 165°F) or you can lightly cut into the center of one of the largest chicken breasts to see if it's cooked to your liking.Once cooked through, use clean tongs to remove that batch of chicken and place on a large baking sheet or platter - and then start another batch. Continue this process until all the chicken is cooked and set aside.
Using the same pan you cooked the chicken in (don't wash it out!), turn the heat down to medium and add the 1 cup of sun-dried tomatoes. Cook for 1-2 minutes until fragrant, while stirring around the pan to release some of the bits from the pan.(note: it's ok if some of the oil from the sun-dried tomatoes gets into the pan, just try to make sure it's not too much, so the sauce doesn't get greasy.) Once the sun-dried tomatoes are warmed through, add the garlic, oregano, red pepper flakes, and black pepper - cook for 1 minute while stirring, so they don't burn.
Then add in 1 cup of heavy cream and 1 cup of chicken broth. Stir until well combined and heat for 2-3 minutes until warmed through.
Once the sauce is warm, add in the parmesan cheese and whisk until creamy. Continue cooking over medium heat for 1-2 minutes until sauce is hot.