Preheat the oven to 375°F (190°C).
Season the chicken thighs evenly with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Heat the olive oil in a large oven-safe skillet or Dutch oven over medium-high heat.
Add the chicken thighs and sear for about 3-4 minutes per side until golden brown but not fully cooked through. Remove the chicken from the skillet and set aside.
Reduce the heat to medium and add the chopped onion to the skillet. Cook for 4-5 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the butter and let it melt completely.
Sprinkle the flour over the onion and garlic mixture and stir continuously for 1-2 minutes to form a roux.
Slowly whisk in the chicken broth, heavy cream, lemon juice, lemon zest, dried thyme, remaining 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Bring the mixture to a gentle simmer and cook for 3-4 minutes until slightly thickened.
Add the rinsed rice to the skillet and stir to combine.
Nestle the seared chicken thighs into the rice mixture, pressing them slightly into the liquid.
Sprinkle the Parmesan cheese evenly over the top.
Cover the skillet tightly with a lid or aluminum foil and transfer to the preheated oven.
Bake for 30 minutes covered, then remove the cover and sprinkle the shredded mozzarella cheese evenly over the casserole.
Return the casserole to the oven uncovered and bake for an additional 10-15 minutes until the rice is tender, the chicken is cooked through (internal temperature 165°F/74°C), and the cheese is melted and golden.
Remove from the oven and let rest for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.