01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish and set aside.
02 - Heat 1 tbsp olive oil in a large skillet over medium heat. Add cubed chicken, season with salt and pepper, and sauté until lightly browned on all sides but not fully cooked through, about 4–5 minutes. Remove and set aside.
03 - Add the remaining 1 tbsp olive oil to the same skillet. Sauté diced onion and minced garlic until fragrant and translucent, about 2 minutes.
04 - Stir asparagus pieces into the skillet and cook for 2–3 minutes until bright green and just tender-crisp.
05 - Reduce heat to low. Add softened cream cheese and heavy cream to the skillet, stirring continuously until smooth and well combined. Season with dried thyme and paprika.
06 - Return the seared chicken to the skillet, tossing to coat evenly with the sauce and vegetables. Simmer gently for 2–3 minutes to meld flavors.
07 - Transfer the entire mixture into the prepared baking dish, spreading it into an even layer. Sprinkle grated Parmesan and shredded mozzarella uniformly over the top.
08 - Bake uncovered for 20–25 minutes, or until the cheese topping is golden and bubbling and the chicken is cooked through to an internal temperature of 165°F.
09 - Remove from oven and let rest for 5 minutes. Garnish with freshly chopped parsley and serve hot.