Preheat oven to 375°F. Grease a 9 x 13-inch baking dish with a little butter. Add the sweet potatoes to the dish and set aside.
Toast the pecans in a dry skillet over medium-low heat for about 4-6 minutes, until golden and fragrant. Transfer to a plate or bowl to cool.
Let the skillet cool for 1-2 minutes, then add the butter. Cook butter over medium-low heat, stirring frequently, until golden brown and has a nutty aroma, about 5-6 minutes. Take care not to burn the butter.
Once browned, add the brown sugar, granulated sugar, cinnamon, nutmeg and salt. Stir to combine. Add water to create a syrup and cook for 1-2 minutes to infuse the flavors. Remove from heat and stir in the vanilla extract.
Pour the butter mixture evenly over the sweet potatoes and toss well to coat. Cover tightly with foil and bake for 30 minutes.
Remove foil and gently stir the sweet potatoes. Continue baking for 20-30 minutes, until the potatoes are fork-tender, but still hold their shape, and the glaze is thick and glossy.
Once the potatoes are tender, stir in ½ cup of toasted pecans. Sprinkle the mini marshmallows evenly over the top.
Bake uncovered for 5-8 minutes, until the marshmallows are puffed and lightly golden. If desired, place under the broiler for 30-60 seconds for a toasty taste and appearance. Keep watch as the marshmallows can burn in a flash.
Sprinkle the remaining pecans over top of the marshmallows. Allow to rest for 5-10 minutes before serving. Spoon some of the buttery glaze over the top.