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Preheat oven to 375 degrees F.
Season chicken with 1 teaspoon salt and ½ teaspoon pepper. Melt 1 tablespoon butter in a large cast iron skillet over medium high heat. Working in batches, add chicken to the skillet in a single layer and cook until golden brown, about 4-5 minutes; set aside.
Melt remaining 4 tablespoons butter. Add onion and celery, and cook, stirring occasionally, until tender, about 3-4 minutes. Stir in garlic until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in wine, scraping any browned bits from the bottom of the skillet.
Stir in chicken stock, heavy cream and Dijon; season with salt and pepper, to taste. Bring to a boil; reduce heat and simmer, stirring often, until reduced and slightly thickened, about 3 minutes.
Remove from heat; stir in cheeses until melted.
Stir in broccoli and chicken until well combined. Sprinkle with topping.
Place into oven and bake until golden brown and bubbling, about 30-35 minutes. Let cool 10-15 minutes.
Serve, garnished with parsley, if desired.
In a small bowl, combine crackers and butter.