Preheat oven to 425°F. Melt butter in a 10-inch cast-iron skillet over medium. Add oil and garlic. Cook, stirring often, until fragrant, 1 minute. Remove from heat. Transfer to a large bowl, reserving 2 tablespoons mixture in skillet. Add potatoes, shallots, salt, and pepper; toss to coat.

Starting in center of skillet, arrange potato and shallot slices in a circular pattern, slightly overlapping slices, until bottom of skillet is covered. Repeat process using remaining potato and shallot. Pour any remaining butter mixture in bowl over potato mixture. Press down firmly in skillet. Place skillet over high heat. Cook, undisturbed, until mixture begins to sizzle, 3 to 4 minutes. Remove from heat.

Bake in preheated oven until potatoes are tender and browned, about 50 minutes. Cool in skillet 20 minutes. Invert onto a serving platter; cut into wedges.