Make the filling: In a medium skillet over medium-high heat, melt the butter the oil. Add the onion and cook, stirring often, until soft, about 5 minutes. Add the celery, broccoli, bell pepper, and green beans and cook, stirring often, until the vegetables are tender, about 10 minutes. Reduce the heat to low. Sprinkle the flour over the vegetable mixture. Cook, stirring constantly, for 2 minutes.
Make the Broth: In glass measuring cup, combine the milk and broth. Slowly add to the vegetable mixture while whisking constantly. The sauce will start to thicken. Add the parsley, tamari, thyme, and sage. Season to taste with salt and pepper. Cook, stirring constantly, until thickened. Remove from the heat, transfer to a 2quart casserole, and set aside.
Make the topping: In a large bowl, mix the flour, salt, baking powder, and baking soda. Using a pastry blender or fork, cut the butter into the flour mixture until it resembles coarse meal. In a measuring cup, combine the buttermilk and honey. Add to the flour mixture, stirring with a fork to form a stiff dough. Add more buttermilk if the dough is too dry. Knead lightly in the bowl for 3 to 5 minutes, until the dough is no longer sticky. Turn the dough out onto a lightly floured surface. Roll out into a shape to cover the casserole dish.
Lay the biscuit topping lightly over the filling. Do not seal the edges. Bake for 20 to 30 minutes, until the crust is golden brown and the filling is bubbling.