Arrange a rack in the middle of the oven and heat the oven to 350ºF. Peel and cut sweet potatoes into 1-inch pieces.

Place the sweet potatoes in a large saucepan and cover with water by about 1 inch. Bring to a low boil and simmer for about 10 minutes.

Using a slotted spoon, transfer the sweet potatoes into an 8x8-inch baking dish, spreading them out in an even layer.

Transfer ¾ cup warm reserved cooking water into a measuring cup. Add brown sugar and stir to dissolve. Add vanilla extract and stir to combine.

Sprinkle ground cinnamon and ground nutmeg over the sweet potatoes.

Pour the water-sugar mixture over the sweet potatoes.

Cut salted butter into cubes and scatter over the sweet potatoes.

Bake for 5 minutes. Remove from the oven and gently toss the sweet potatoes to combine the sauce.

Bake until fork-tender, about 10 minutes more. Spoon the candied mixture evenly over the top.

Let the candied yams cool for about 5 minutes so the sauce can thicken. Serve warm.