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 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 chicken to a plate and set aside.
03 - Add the remaining 1 tbsp olive oil to the same skillet. Sauté diced onion and minced garlic over medium heat until fragrant and translucent, about 2 minutes.
04 - Add asparagus pieces to the skillet and cook for 2–3 minutes, stirring occasionally, until bright green and just barely tender.
05 - Reduce heat to low. Add 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. Stir to coat evenly in the sauce and simmer gently for 2–3 minutes.
07 - Transfer the entire mixture to 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 bubbly and golden brown 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.