Preheat your oven to 400°F (200°C).
Place the unsalted butter in a 9x13-inch baking dish and set it in the oven for 3 to 5 minutes until the butter is completely melted.
Remove the dish from the oven and evenly distribute the shredded rotisserie chicken over the melted butter.
Spread the chopped yellow onion and the frozen mixed vegetables over the chicken layer in an even thickness; do not stir the ingredients.
In a medium mixing bowl, whisk together the buttermilk biscuit mix, whole milk, and shredded sharp cheddar cheese until just combined, then pour this mixture evenly over the vegetable layer.
In a separate bowl or large measuring cup, whisk the chicken stock, cornstarch, garlic powder, dried parsley, smoked paprika, salt, and black pepper until the cornstarch is fully dissolved and no lumps remain.
Carefully pour the seasoned stock mixture over the biscuit layer, ensuring it covers the surface; do not stir the layers together.
Transfer the dish to the middle rack of the oven and bake for 40 to 45 minutes, or until the cobbler topping is puffed, set, and deep golden brown.
Remove from the oven and let the dish rest for 10 minutes before serving to allow the internal sauce to thicken to the proper consistency.