Although impressive-looking, these potatoes couldn't be simpler. The finishing touch? A coating of sage butter.
Preheat oven to 375 degrees. Make deep cuts into each potato, 1/4 inch apart, without completely cutting through. Place shallots in each cut (using about half the shallots) and season with salt and pepper. Arrange potatoes, cut sides down, in a 9-by-13-inch baking dish; dot with 2 tablespoons butter. Scatter remaining shallots around potatoes.
Tightly cover dish with foil and bake until potatoes are tender, about 40 minutes, flipping halfway through.
Uncover and bake 15 minutes. Meanwhile, combine sage and remaining 2 tablespoons butter. Increase oven temperature to 450 degrees. Top potatoes with sage butter; scoop up loose shallots and divide among potatoes, then bake until golden and crisp, 10 to 15 minutes more.
To prep ahead, bake through step 2. Let cool, cover, and refrigerate, up to 2 days. Let sit at room temperature 1 hour before proceeding as directed.