Preheat the oven to 375°F.

Peel the sweet potatoes and slice them evenly into 1/4-inch rounds. Maintaining an even thickness helps the potatoes become tender without losing their shape during baking.

In a small bowl, thoroughly combine the packed brown sugar, kosher salt, cinnamon, nutmeg, and ginger so the seasonings are evenly distributed throughout the sugar.

Arrange the sliced sweet potatoes in a baking dish, overlapping them slightly where necessary. Distribute the small pieces of unsalted butter across the potatoes, then scatter the brown sugar and spice mixture evenly over the surface.

Cover the baking dish securely with aluminum foil. Bake for 30 minutes, allowing the trapped steam to soften the sweet potatoes while the melting butter and brown sugar begin forming a rich glaze.

Carefully remove the foil, taking care to avoid the escaping steam. Gently stir the potatoes to redistribute the developing syrup and coat the slices more evenly.

Return the uncovered dish to the oven and continue baking for 20 minutes. During this period, the glaze will reduce and become more concentrated while the sweet potatoes develop lightly caramelized edges. Gently stir once halfway through this stage to maintain an even coating.

Remove the baking dish from the oven and change the oven setting to broil.

Spread the miniature marshmallows evenly across the hot sweet potatoes. Place the dish beneath the broiler for approximately 30 seconds, monitoring it continuously, until the marshmallows soften and develop a pale golden-brown surface.