Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a baking dish.

Arrange yams in the prepared baking dish. Combine brown sugar, 1/2 of the melted butter, and vanilla extract in a small bowl; pour evenly over yams. Cover the baking dish.

Bake in the preheated oven for 30 minutes. Remove and coat with remaining butter. Cover and bake for an additional 30 minutes. Remove the cover, top with marshmallows, and bake until marshmallows are melted, 5 more minutes.