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 the cubed chicken, season with salt and pepper, and sauté until lightly browned on the outside but not fully cooked through, about 4–5 minutes. Remove the chicken from the skillet and set aside.
03 - Add the remaining 1 tbsp olive oil to the same skillet. Sauté the diced onion and minced garlic until fragrant and translucent, about 2 minutes.
04 - Stir in the trimmed asparagus pieces and cook for 2–3 minutes until bright green and just tender.
05 - Reduce heat to low. Add the 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, folding it into the cream sauce and vegetables. Let the mixture simmer gently for 2–3 minutes so the flavors meld together.
07 - Transfer the entire skillet mixture to the prepared baking dish, spreading it out evenly. Sprinkle the 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 the oven and let rest for 5 minutes. Garnish with chopped fresh parsley and serve hot.