01 - Preheat oven to 400°F (200°C). Lightly grease a 9×12-inch baking dish and set aside.
02 - Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the cubed chicken, season with salt and pepper, and sauté until lightly browned on all sides but not fully cooked through, about 4–5 minutes. Transfer chicken to a plate and set aside.
03 - Add the remaining 1 tablespoon olive oil to the same skillet. Sauté the diced onion and minced garlic until fragrant and translucent, about 2 minutes.
04 - Stir the asparagus pieces into the skillet and cook for 2–3 minutes until bright green and just tender-crisp.
05 - Reduce heat to low. Add the softened cream cheese and heavy cream to the skillet, stirring constantly until the mixture is 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 into the prepared baking dish, spreading it 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 brown and bubbling and the chicken is cooked through to an internal temperature of 165°F (74°C).
09 - Remove from the oven and let rest for 5 minutes. Garnish with freshly chopped parsley and serve hot.