Preheat your oven to 375°F and lightly grease a 9x13 inch baking dish. While the oven heats, cut the chicken breasts into 1-inch chunks and season generously with salt and pepper. Remove the cream cheese from the refrigerator if you haven't already—it should be at room temperature for easier mixing. Crumble the cooked bacon into roughly 1/2-inch pieces and thinly slice the green onions, keeping the white and green parts separate for better texture control.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Working in batches if needed to avoid crowding, cook the seasoned chicken pieces for 3-4 minutes per side until golden brown on the outside—the chicken doesn't need to be cooked through at this point. Transfer the seared chicken to your prepared baking dish, spreading it in an even layer.
In a medium bowl, combine the softened cream cheese, ranch seasoning, and sour cream, stirring until smooth and well-blended. I find that adding the ranch seasoning directly to the cream cheese first before incorporating the sour cream gives a more even flavor distribution. Spread this mixture evenly over the seared chicken in the baking dish, then scatter the first half of the crumbled bacon over the sauce.
Combine the shredded cheddar and mozzarella cheeses and sprinkle evenly over the cream cheese mixture—using cheese shredded from a block rather than pre-shredded gives you better melting and a creamier final result. Bake uncovered at 375°F for 20-25 minutes until the cheese is melted and bubbly around the edges.
For a golden, slightly crispy cheese top, carefully transfer the casserole to the broiler for 2-3 minutes—watch closely as broilers can brown quickly. Remove from the oven and let rest for 5 minutes, which allows the sauce to set slightly and the chicken to finish cooking gently. Top the casserole with the remaining crumbled bacon, the white parts of the green onions first for a milder onion flavor, then the green parts, and finish with a light sprinkle of fresh parsley for color and freshness.