Preheat oven to 350°F. Spray a 3-quart baking dish with cooking spray.
Thaw the 1 (10 to 12-ounce) bag frozen broccoli florets and pat dry with paper towels; set aside.
In a large skillet over medium heat, melt 1/2 cup salted butter. Add 1 cup diced onion and 1 garlic clove, minced; cook, stirring occasionally, until the onion is softened (about 4–5 minutes).
Whisk in 1/3 cup all-purpose flour and cook, whisking, for 1 minute.
Gradually whisk in 1 cup chicken broth and 1 cup milk until smooth. Bring the sauce to a simmer, then add 1/2 teaspoon black pepper and seasoned salt to taste. Simmer 2–3 minutes until the sauce is slightly thickened.
Reduce heat to low and add 8 ounces cream cheese, cubed and softened. Stir until the cream cheese is fully melted and the sauce is smooth.
Stir in 3 to 4 cups shredded cooked chicken, the thawed and patted-dry broccoli, and 1 tablespoon poppy seeds. Mix until combined and heated through; adjust seasoned salt if needed.
Spread 2 cups cooked white rice in an even layer in the prepared baking dish. (If desired, lightly sprinkle a little seasoned salt over the rice.)
Spoon the chicken–broccoli mixture evenly over the rice.
In a bowl, combine 2 tablespoons melted butter with 2 cups coarsely crushed Ritz crackers until the crumbs are moistened. Evenly sprinkle the crumb mixture over the top of the casserole.
Bake in the preheated 350°F oven for 25 minutes, until heated through and the topping is golden. Let rest a few minutes before serving.