Cook sweet potatoes,Yukon Gold potatoes and squash in a large pot of salted, boiling water until fork tender. Drain well. Set aside for 10 minutes to cool slightly. Mash until a desired consistency is achieved.
Preheat oven to 350°F (180°C). Return empty pot to stove set over medium heat. Add soup, milk, butter, ginger (if using), salt, pepper, cinnamon, allspice, nutmeg and cloves.
Cook, stirring, until simmering. Fold in mashed vegetables until just combined. Cool slightly. Stir in beaten egg. Scrape mashed vegetables into buttered 9-inch (2.5 L) square dish.
Topping: Sprinkle evenly with marshmallows. Toss pecans with brown sugar and butter. Scatter over the marshmallows. Bake for 15 to 20 minutes or until heated through and marshmallows are golden brown.