Put the potato slices in a large bowl, and toss them with the melted butter. Then pour the vegetable oil into a well-seasoned, 10-inch-diameter cast iron skillet (or oven-proof non-stick skillet), and swirl to coat the bottom. In the center of the skillet, arrange 4 potato slices in an overlapping circle. Arrange more slices in a clockwise, overlapping circle that extends to the skillet's edge. Dust this first layer with a pinch each of the salt, pepper, and (optional) chives. Working counter-clockwise, arrange another overlapping layer of potatoes, seasonings, and chives. Continue layering the potatoes in alternating circles, dusting all but the final layer with the seasonings and chives. When you are finished, you will have 6 or more potato layers in your skillet.
Set the skillet over medium-low heat. When the oil begins to sizzle (listen carefully!), press down on the potatoes with an 8- or 9-inch-diameter cake pan to compress them slightly. Then cover the skillet and cook, still over medium-low heat, for exactly 10 minutes. Meanwhile, center the oven rack and preheat the oven to 450°F.
Remove the lid, and transfer the skillet to the preheated oven. Bake until the potatoes are tender when pierced with a skewer -- about 30 minutes. Then, while holding the handle of the skillet with your mitted hand, and while holding the cake pan over the potatoes with your other hand, tilt the skillet over the kitchen sink (or a bowl) to drain off excess fat.
Place a carving board or serving platter over the skillet, and invert the two to unmold. Then cut the cake into 8 equal servings. Delicious hot, warm, or at room temperature.