Wash hands with soap and water.
Heat 2 teaspoons of the olive oil in a large skillet over medium-high heat.
Scrub onion with a clean vegetable brush under running water.
Season chicken breasts with the Italian seasoning, salt and pepper. (Do not rinse raw poultry or meat.) Add to pan and sear for 4 minutes on each side, until golden brown. Wash hands with soap and water after handling uncooked chicken.
Remove chicken breasts from the skillet to a plate and cover with aluminum foil to keep warm. (They will finish cooking later.)
Reduce heat to medium and add remaining teaspoon olive oil to pan.
Add diced onion and cook, stirring occasionally, for 4-5 minutes, until softened. Add garlic and sun-dried tomatoes and sauté for 30 more seconds.
Add chicken broth and cream cheese and stir until melted.
Return the chicken breasts to the skillet, along with any accumulated juices, and turn to coat them in the sauce. Top the chicken breasts with the mozzarella cheese (about ¼cup for each one).
Cover the pan, reduce the heat to medium-low and cook for 7-9 minutes, until the internal temperature reaches 165 ºF on food thermometer. (Exact cook time will depend on how thick your chicken breasts are.)
Serve chicken breasts with extra sauce spooned over the top and enjoy!