Preheat oven to 350º F (176°C). Start the rice, grain, or biscuits if serving over them.
Peel and dice the onion and mince the garlic. Heat 1 1/2 cups of vegan broth and have it ready to add. Chop broccoli florets and vegan chicken into bite-sized pieces.
Make the filling
Sauté the onion and garlic in oil for about 5 minutes until the onion becomes translucent.
Sprinkle the onion mixture with flour and stir well until it becomes incorporated. Slowly pour in the warm broth a little at a time stirring continuously. Then pour in the plant-based milk and stir again until thick and creamy.
Stir in vegan sour cream, poppy seeds, soy sauce, and salt and black pepper to taste.
Add in the broccoli and vegan shredded chicken and stir well. (If not baking in the skillet, spray a 9 x 13 baking dish with cooking spray and pour the mixture into it.)
Make the topping
Melt vegan butter in a bowl, then crumble a tube of crackers and pour it into the melted butter.
Sprinkle the top of your casserole with the buttery crackers and bake for 20 minutes until bubbly and golden brown.