Preheat oven to 350 degrees F. Grease a 9-inch cake pan.
Make the sweet potato cake. Peel and cut about 2 medium sweet potatoes. Place in a pot and add enough water to cover the potatoes. Cover the pot, bring to a boil over medium-high heat and continue to cook until the potatoes are fork-tender. Drain and mash the potatoes. Let cool completely.
Whisk together 1 cup of the sweet mashed potatoes with brown sugar, oil, yogurt, maple syrup, 2 eggs, and vanilla until well combined. In a separate bowl, combine the flour with the baking powder, baking soda, salt, cinnamon, nutmeg, cloves, and allspice. Add the wet ingredients to the dry ingredients, stirring just until combined.
Pour the batter into the greased cake pan and bake for 35-40 minutes or a toothpick inserted in the center comes out clean. Place the cake on a wire rack and let cool completely.
Meanwhile, make the marshmallow meringue. Whisk together 4 egg whites with brown sugar and honey. Heat the egg mixture over a double boiler until the temperature reads 160 degrees F. Transfer the egg whites to a mixing bowl and add the vanilla extract. Beat the mixture with a whisk at high speed for 5-7 minutes or until stiff peaks form.
Spread the meringue on the sweet potato cake and torch the meringue until lightly browned. Serve immediately.