Preheat the oven:
Preheat your oven to 400°F (200°C). Grease a 9×13-inch baking dish with cooking spray or butter.

Cook the filling:
In a large saucepan, melt the butter over medium heat. Add the chopped onion and sauté until soft and translucent, about 3-4 minutes. Stir in the garlic and cook for 1 more minute.

Make the sauce:
Sprinkle the flour over the onion mixture and whisk to combine, cooking for 1-2 minutes until the raw flour taste is gone. Gradually pour in the chicken broth, whisking constantly to avoid lumps. Then, stir in the milk and cook until the sauce thickens, about 3-4 minutes.

Season and add vegetables:
Stir in the thyme, parsley, salt, and pepper. Add the thawed mixed vegetables and shredded chicken to the sauce. Mix everything well and simmer for 2 minutes. Pour the filling into the prepared baking dish and spread evenly.

Prepare the topping:
In a medium bowl, combine the baking mix, milk, and cheddar cheese (if using). Mix until just combined, being careful not to overmix. The dough should be slightly thick and spoonable.

Add the topping:
Drop spoonfuls of the biscuit dough evenly over the filling in the baking dish. Spread the dough lightly with a spoon if needed, but it’s okay if some gaps remain—this allows the sauce to bubble through while baking.

Bake:
Place the casserole in the preheated oven and bake for 25-30 minutes, or until the biscuit topping is golden brown and cooked through. Let the casserole rest for 5-10 minutes before serving.