Preheat the oven to 350°F (175°C).
Peel and cube the sweet potatoes, then boil them in water for 15 minutes or until they are tender when pierced with a fork.
Drain the sweet potatoes and mash them in a large bowl with a hand masher or an electric mixer until they are smooth.
Add the brown sugar, granulated sugar, whole milk, eggs, kosher salt, nutmeg, cinnamon, and vanilla extract to the bowl with the mashed sweet potatoes. Mix until well combined.
Stir in the melted unsalted butter until it is fully incorporated.
Transfer the sweet potato mixture to a 9x13 inch baking dish.
Sprinkle the chopped pecans over the top of the sweet potato mixture.
Bake the casserole in the preheated oven for 25 minutes.
Remove the casserole from the oven and top it with the mini marshmallows.
Return the casserole to the oven and bake for an additional 5-10 minutes, or until the marshmallows are golden brown.