Preheat oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish with cooking spray.
Pierce the sweet potatoes with a fork and bake directly on the oven rack for about 45-50 minutes, or until tender when pierced. Let cool slightly.
Once cool enough to handle, peel the sweet potatoes and mash them in a large bowl until smooth.
Add evaporated milk, sweetened condensed milk, eggs, softened butter, brown sugar, cinnamon, vanilla extract, allspice, nutmeg, cloves, ginger, and salt to the mashed sweet potatoes. Mix until well combined and creamy.
Spread the sweet potato mixture evenly into the prepared baking dish.
For the crumble topping, combine the chopped pecans, coconut flakes, flour, and remaining brown sugar in a medium bowl. Cut in the remaining butter until the mixture is crumbly and well blended.
Sprinkle the coconut-pecan crumble evenly over the sweet potato layer.
Bake the casserole uncovered for 30 minutes.
Remove the casserole from the oven and evenly sprinkle mini marshmallows over the top.
Return to the oven and bake for an additional 10-15 minutes, or until the marshmallows are golden and toasted.
Remove and let cool for 10 minutes before serving. Enjoy this decadent Southern classic!