In a large Dutch oven, melt butter over medium heat. Add onion and garlic; cook, stirring occasionally, until tender, about 5 minutes. Whisk in flour; cook for 2 minutes, whisking constantly. Gradually whisk in broth; bring to a boil. Reduce heat to medium-low; cook, whisking constantly, until thickened, about 2 minutes.
Remove from heat; whisk in cream cheese, poppy seeds, thyme, mustard, salt, zest, and pepper until smooth. Stir in chicken, rice, and broccoli; transfer to prepared pan.
In a small bowl, stir together crackers and melted butter; sprinkle over chicken mixture.
Preheat oven to 350°. Bake until golden brown and bubbly, 25 to 30 minutes, covering with foil to prevent excess browning, if necessary. Let stand for 10 minutes before serving.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/chicken-poppy-seed-rice-casserole/