Heat your olive oil in a large skillet over medium-high heat. Pat your chicken breasts dry with paper towels—this helps them get a nice golden sear instead of steaming. Once the oil shimmers, add the chicken and sear for 3-4 minutes per side until golden brown. Don't flip it around constantly (I learned that the hard way).
Remove the chicken to a clean plate and set it aside. The chicken doesn't need to be fully cooked through yet—it'll finish in the sauce. You'll see all those golden bits stuck to the bottom of the pan, and that's liquid gold for flavor.
In the same skillet, add your diced onion and minced garlic to the remaining oil. Cook for about 2 minutes, stirring frequently, until fragrant and the onion starts getting soft. This is the foundation of your creamy sun dried tomato chicken family sauce, so don't skip it.
Pour in the chicken broth and add the sun-dried tomatoes, oregano, basil, and black pepper. Stir everything together and let it simmer for 3-4 minutes to let the flavors wake up. The kitchen smells absolutely amazing at this point—my 6-year-old usually wanders in asking what's for dinner.
Reduce the heat to medium and pour in the heavy cream while stirring constantly. Add the chicken back to the skillet and nestle it into the sauce. You want the chicken fully submerged or mostly covered so it cooks evenly.
Let everything simmer for 8-10 minutes until the chicken reaches an internal temperature of 165°F. I check it with a meat thermometer at the thickest part. Once it hits that temp, sprinkle the mozzarella cheese over everything and stir gently.
Finish with the lemon juice right at the end—it brightens up all those rich, creamy flavors and keeps the dish from feeling too heavy. Taste it and adjust the pepper or salt as needed. Honestly, this final squeeze of lemon is what makes people ask for the recipe.