Preheat your oven to 375°F (190°C).
Peel the sweet potatoes with a sharp vegetable peeler and rinse under cold water. Cut them into rounds about half an inch thick, keeping them as uniform as possible. If you have thick potatoes, cut the rounds in half to make half-moons.
Place all sliced sweet potatoes in a 9x13-inch baking dish in a somewhat even layer. They can overlap slightly.
Melt the butter in a medium saucepan over low heat. Once melted, remove from heat and add the maple syrup, brown sugar, cinnamon, nutmeg, orange zest, vanilla extract, and salt. Whisk until completely smooth.
Pour the glaze over the sweet potatoes and toss gently until every piece is coated.
Cover the baking dish tightly with aluminum foil and bake for 25 minutes.
Carefully remove the foil (watch out for hot steam) and give the potatoes a gentle stir.
Return the dish to the oven uncovered and bake for 20 minutes. Stir again.
Continue baking uncovered for another 25 to 30 minutes, until the sweet potatoes are tender when pierced with a fork and the glaze is thick and glossy.
Remove from the oven and let rest for 10 minutes before serving. The glaze will thicken further as it cools.