Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
Pat the chicken breasts dry with paper towels, then season them with salt and pepper.
Heat olive oil in a large oven-safe skillet over medium-high heat. Add the chicken breasts and sear them for 3-4 minutes on each side until they have a golden crust. Place them in the prepared baking dish.
In a bowl, mix together the softened cream cheese, ranch seasoning mix, and sour cream or Greek yogurt until well combined.
Spread the cream cheese mixture evenly over the seared chicken breasts in the baking dish. Sprinkle half of the cooked, chopped bacon on top of the cream cheese layer.
Top with both the shredded cheddar and mozzarella cheeses.
Place the baking dish in the preheated oven and bake for 20-25 minutes, or until the chicken is cooked through and the cheese is melted and bubbly. If desired, switch the oven to broil for the last 2-3 minutes to brown the cheese topping. Keep an eye on it to prevent burning.
Remove the baking dish from the oven and let it rest for a few minutes before serving. Garnish with the remaining bacon, chopped green onions, and if using, fresh parsley.