Step 1: Preheat the oven to 375°F (190°C). Grease a 9×13 inch baking dish.
Step 2: In a large skillet, heat olive oil over medium-high heat. Add chicken cubes and cook until browned and cooked through, about 8-10 minutes. Remove chicken and set aside.
Step 3: In the same skillet, add onion and garlic. Cook until softened, about 3-4 minutes.
Step 4: Add spinach to the skillet and cook until wilted, about 2-3 minutes. Stir in heavy cream and chicken broth, then bring to a simmer.
Step 5: Return the cooked chicken to the skillet. Add thyme, salt, and pepper. Stir well to combine.
Step 6: Transfer the mixture to the prepared baking dish. Sprinkle mozzarella and Parmesan cheeses evenly over the top.
Step 7: In a small bowl, mix breadcrumbs with melted butter. Sprinkle the breadcrumb mixture over the cheese.
Step 8: Bake in the preheated oven for 20-25 minutes, until the top is golden brown and bubbly.
Step 9: Let the casserole cool for 5 minutes before serving.