Pat the chicken breasts dry with a paper towel so they sear properly instead of steaming in the pan. Season both sides generously with salt and pepper. This step matters more than people think, since underseasoned chicken makes the whole dish taste flat later on.
Heat olive oil in your oven-safe skillet over medium-high heat until it shimmers. Add the chicken and cook for 3-4 minutes per side, just until golden brown on the outside. It doesn't need to be fully cooked through yet, since it will finish roasting in the oven.
In a mixing bowl, combine the softened cream cheese, sour cream, chopped spinach, artichokes, half the mozzarella, Parmesan, garlic, and lemon juice. Stir until everything is evenly distributed and creamy. This mixture is essentially your favorite dip, just built to top a chicken breast.
Spread the spinach artichoke mixture evenly over each seared chicken breast in the skillet. Sprinkle the remaining mozzarella on top so it forms a golden, bubbly crust as it bakes. If you're using red pepper flakes, this is the moment to scatter them on.
Transfer the skillet to a 400°F oven and bake for 15-18 minutes, until the chicken reaches an internal temperature of 165°F and the top is bubbling and lightly browned. Use a meat thermometer to double check, since chicken thickness can vary a lot between breasts.
Let the chicken rest for about 5 minutes before serving. This keeps the juices inside the meat instead of spilling out onto your cutting board. Then plate it up while the cheese is still melty and inviting.