01 - Preheat oven to 400°F. Lightly grease a 9×13-inch baking dish and set aside.
02 - Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add the cubed chicken, season with salt and pepper, and sauté until lightly golden on all sides but not fully cooked through, about 4–5 minutes. Transfer to a plate and set aside.
03 - Add the remaining 1 tbsp olive oil to the same skillet. Sauté the diced onion and minced garlic over medium heat until softened and fragrant, about 2 minutes.
04 - Stir the asparagus pieces into the skillet and cook for 2–3 minutes until bright green and just barely tender.
05 - Reduce heat to low. Add the softened cream cheese and heavy cream to the skillet, stirring constantly until smooth and well combined. Season with dried thyme and paprika.
06 - Return the seared chicken and any accumulated juices to the skillet. Toss to coat evenly with the sauce and vegetables. Let simmer gently for 2–3 minutes so flavors meld together.
07 - Transfer the entire mixture into the prepared baking dish, spreading it into an even layer. Sprinkle the grated Parmesan and shredded mozzarella uniformly over the top.
08 - Bake uncovered for 20–25 minutes, until the cheese topping is bubbling and golden brown and the chicken is cooked through to an internal temperature of 165°F.
09 - Remove from the oven and let rest for 5 minutes. Garnish with freshly chopped parsley and serve warm.