01 - Preheat oven to 400°F (200°C). Lightly grease a 9×13-inch baking dish and set aside.
02 - Heat 1 tablespoon of 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 the outside but not fully cooked through, about 4–5 minutes. Transfer the chicken to a plate and set aside.
03 - Add the remaining 1 tablespoon of olive oil to the same skillet. Sauté the diced onion and minced garlic over medium heat 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 creamy sauce and vegetables. Let the mixture simmer gently for 2–3 minutes so the 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 evenly across the top.
08 - Bake uncovered for 20–25 minutes, or until the cheese topping is deeply golden and bubbling and the chicken is cooked through to an internal temperature of 165°F (74°C).
09 - Remove from the oven and let the bake rest for 5 minutes. Garnish with chopped fresh parsley and serve hot.