Heat oven to 425ºF with rack set in middle position; place a large cast-iron skillet on middle rack while oven preheats.

Wash and thoroughly dry potatoes.

Cut potatoes in half lengthwise then place cut side down on a cutting board. Working with one half at a time, arrange wood skewers or chopsticks along length of potato half. Cut ⅛-inch slices crosswise (top to bottom) nearly all the way through the potato (about 80% of the way through), stopping before you cut through the bottom (the wood skewers should act like bumpers and keep your knife from slicing all the way through).

Carefully remove skillet from oven and drizzle 1 tablespoon oil in pan; swirl to coat. Gently arrange sweet potato halves, cut side down, in a single layer; drizzle ½ teaspoon oil over each potato half and sprinkle with salt and pepper.

Return skillet to oven and back sweet potatoes 30 minutes.

Meanwhile, melt butter in a small saucepan over medium-low heat; stir in 1 teaspoon salt, garlic, and nutmeg. Cook until fragrant and bubbly, about 30 seconds. Off heat, stir in sage.

Remove sweet potatoes from oven and separate slices using a fork or knife. Fit a few slices of shallot between sweet potato slices (3 or 4 per potato); spoon butter mixture evenly over potatoes.

Return skillet to oven and back potatoes 10 minutes more. Turn oven to broil and broil potatoes 2–4 minutes, until edges are crispy and charred.