In a medium bowl, mix the softened cream cheese and pesto sauce until well combined.
Season the chicken breasts with salt and pepper on both sides.
In a large oven-safe skillet, heat the olive oil over medium-high heat. Once hot, add the chicken breasts and sear for about 3-4 minutes on each side until golden brown.
Once seared, remove the skillet from heat and spread the cream cheese and pesto mixture evenly over the top of each chicken breast.
Sprinkle the shredded mozzarella and grated Parmesan cheese over the chicken and top with the chopped spinach.
Transfer the skillet to the preheated oven and bake for 25-30 minutes, or until the chicken is cooked through and the cheeses are bubbly and slightly golden.
Remove from oven and let it rest for a few minutes before serving.