In a large saucepan, combine the potatoes with enough cold water to cover by 1 inch. Bring to a boil over high heat, reduce the heat and simmer actively for about 10 minutes, or until the potatoes are just tender.
While the potatoes are cooking, in a large heavy skillet, heat the butter and olive oil over medium heat. Add the onions and saute, stirring occasionally, for 5 minutes, or until softened. Season with salt and pepper and remove from the heat.
Remove the potatoes from the heat, drain and, when cool enough to handle, slice the potatoes 1/4" thick.
Preheat the oven to 425°F In a small bowl, combine the garlic and italian seasoning and toss together to mix evenly.
Grease a 9x13 baking dish and place one layer of sliced potatoes, slightly overlapping, in the bottom. Distribute about 1/4 of the sliced onions evenly over the potatoes, then scatter a little of the garlic herb mixture over the top and drizzle with a little olive oil. Repeat until all the potatoes, onions, and garlic mixture have been used up, finishing with a layer of the olive oil and herb mixture.
Pour the chicken stock around the edges of the pan so as not to disturb the herb topping, and cover with aluminum foil. Bake 30 minutes, until the potatoes are tender.
Remove the foil and scatter the cheese over top. cook for 10 minutes more.