01 - Heat olive oil and butter in a large skillet over medium heat. Season chicken breasts evenly with salt and pepper. Place chicken in the skillet and sear for 3 to 4 minutes per side until a golden-brown crust forms. Remove chicken from the pan and set aside on a plate.
02 - In the same skillet, add the chopped onion and cook for 2 to 3 minutes until softened and translucent. Add the minced garlic and sauté for 1 additional minute, stirring frequently to prevent burning.
03 - Add the softened cream cheese, milk, and grated Parmesan to the skillet. Whisk continuously until a smooth, uniform sauce forms with no lumps remaining. Stir in the dried Italian herbs until evenly incorporated.
04 - Return the seared chicken breasts to the skillet, nestling them into the sauce. Spoon the sauce over each piece to coat evenly. Reduce heat to low, cover the skillet with a lid, and simmer gently for 15 to 18 minutes until the chicken reaches an internal temperature of 165°F and is fully cooked through.
05 - Remove the skillet from heat and sprinkle the chicken generously with fresh chives or parsley. Serve immediately while hot, spooning additional sauce from the pan over each portion.