Preheat the oven to 425 degrees Fahrenheit. In a 10-inch cast-iron skillet over medium heat, melt the butter. Pour in the oil and garlic. Cook, stirring frequently, for 1 minute, or until fragrant. Take the pan off the heat. Transfer to a large mixing bowl, reserving 2 tablespoons of the mixture in the skillet. Toss in the potatoes, shallots, salt, and pepper to coat.

Starting in the center of the skillet, arrange potato and shallot slices in a circular pattern, slightly overlapping slices, until the bottom is covered. Repeat with the remaining potato and shallot. Any remaining butter mixture in the bowl should be poured over the potato mixture. Firmly press down in skillet. Preheat a skillet over high heat. Cook, stirring occasionally, until the mixture begins to sizzle, 3 to 4 minutes. Take the pan off the heat.

Bake in a preheated oven for 50 minutes, or until potatoes are tender and browned. Allow to cool in the skillet for 20 minutes. Invert onto a platter and cut into wedges.