Step 1

Make the potatoes: Place a baking sheet near the stove. In a large, high-sided skillet over medium-high heat, heat 1 tablespoon of the oil until it shimmers. Cover the bottom of the pan with a single layer of the potatoes — a little overlapping is okay — and lightly season with salt and pepper. Cook, undisturbed, until the potatoes start to blister and brown, 1 to 2 minutes per side, peeking with a spatula and adjusting the heat as needed. Watch carefully so the potatoes don’t burn and overcook — they should remain firm. Transfer to the baking sheet and repeat with the remaining potatoes, adding more oil and adjusting the heat as needed.

Step 2

Reduce the heat to medium, and add the remaining 1 tablespoon of oil to the skillet, followed by the onions, and cook, stirring frequently, until softened and starting to turn golden, about 5 minutes. Add the chopped sage and garlic, lightly season with salt and pepper, and cook, stirring frequently, until fragrant, about 1 minute.

Step 3

Return the potatoes to the skillet and gently stir to thoroughly combine with the onion. Pour the wine, broth or water over the potatoes and quickly cover the skillet with a lid or foil. Reduce the heat to medium-low and cook until the potatoes are fork-tender, 8 to 10 minutes, checking the thickest pieces and stirring about halfway through the cooking time.If you like, transfer the potatoes to a serving platter or serve them directly from the skillet.

Step 4

Make the garnish: If serving with fried sage leaves, when the potatoes are almost ready, add the butter or olive oil to a small skillet over medium heat. (If using butter, swirl it in the pan as it melts. Once the foam dissipates and it starts to smell nutty, look for brown bits to form in the bottom, about 2 minutes. If using the oil, heat it until it shimmers.) Add the sage leaves and fry until they start to curl and look crisp, 10 to 20 seconds. Remove from the heat. (If the potatoes need to cook more, transfer the butter/oil and sage leaves to a heatproof bowl to stop the cooking.)

Step 5

Just before serving, pour the warm brown butter or oil with the sage leaves, if using, over the potatoes and sprinkle with the toasted nuts. Serve warm.