Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, usually around 9-11 minutes. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add the diced chicken breast and season with salt, pepper, and dried thyme. Cook until golden and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant. Pour in the chicken broth, heavy cream, lemon zest, and lemon juice. Stir well and bring the mixture to a gentle simmer. Let it cook for 3-4 minutes to thicken slightly.
Reduce heat to low. Stir in the grated Parmesan cheese until melted and the sauce is creamy and smooth. Add the cooked penne, sautéed chicken, and fresh spinach to the skillet. Toss everything together to coat evenly and wilt the spinach.
Preheat your oven to 375°F (190°C). Transfer the creamy mixture into a greased baking dish. Sprinkle the breadcrumbs evenly over the top for a crispy golden crust.
Bake uncovered for 20-25 minutes until the top is golden and bubbly. Remove from the oven and sprinkle with chopped parsley before serving.