PREP: Using a mallet, pound down the chicken breastsso that they all cook in the same amount of time, alternately, you can slice the chicken breasts horizontally if the filets are very thick. This is optional, but the chicken is much easier to prepare this way. Sprinkle the chicken with 1 teaspoon of kosher salt.
COOK: Heat a tablespoon of olive oil and a tbsp of butter in a large skillet over medium-high heat. When the oil is hot, add the chicken breasts and cook them for roughly 3-5 minutes per side or until they’re cooked through to a minimum of 160ºF. Remove the chicken to a plate; cover loosely with foil, so the chicken finishes cooking through.
SAUCE: Add the remaining tablespoon of olive oil and butter to the same skillet lowering the heat to medium. Saute the shallots for 3 minutes. Then add the garlic and continue to cook for another 1 minute. When the onions are translucent, add the red pepper flakes, Italian seasoning, and chicken broth. Let the broth simmer for 5-7 minutes or until it reduces down to about ½ cup. The wider the cooking vessel, the quicker this will happen.
FINISH: Then add the heavy cream, parmesan, and sun-dried tomatoes; stir to combine. Bring to a simmer, without letting the cream boil. Taste and adjust the salt as needed. Add the chicken breasts back to the skillet and let them simmer in the sauce for 1-2 minutes. Top with basil and serve warm with sautéed broccoli, over mashed potatoes, with rice, or pasta.