Heat the butter and olive oil in a 12" cast iron pan over medium-high heat. When the butter is melted, add the onion and garlic, and the salt and pepper to taste. Sauté until the onions have softened, about 1-2 minutes.
Whisk in the flour and cook until lightly browned, about 1-2 minutes. Gradually whisk in the chicken stock, heavy whipping cream, cooking wine, Italian seasoning, and paprika; cook, while whisking, until the mixture starts to thicken, about 5 minutes.
Mix in the chicken, vegetables, parsley, and bay leaves. Simmer over medium-low heat for 15 minutes. Season with salt and pepper to taste.
Meanwhile, preheat the oven to 400 F. If you are using a skillet that is not safe for the oven, transfer the filling to a baking dish at this point.
Remove the bay leaves and place the biscuits evenly on top of the filling. Brush the biscuits with the egg and sprinkle with sea salt.
Bake on the center rack until golden, about 25-30 minutes. Check the bottom of one biscuit to make sure it's are cooked through before removing from the oven, then allow it to cool for about 10 minutes before serving.
To serve, scoop the filling into a bowl and top with a biscuit.