Preheat oven to 350 degrees F. Liberally grease a 13x9" rectangular baking pan with cooking spray and set aside briefly.
In a large bowl with an electric mixer, beat together the granulated sugar and sweet potato puree until blended. Carefully beat in the oil and vanilla, then the eggs one at a time, beating well after each addition.
Meanwhile, in a separate bowl, whisk together the flour, baking powder, baking soda, spices, and salt. Gradually add in the flour mixture to the wet mixture, beating well until batter is smooth and combined. Pour the batter into the prepared pan and smooth out the top. Bake for approximately 25-30 minutes or until a toothpick inserted near the center comes out clean or with moist - not wet - crumbs. Cool completely.
For the frosting: In the bowl of a stand mixer, cream together the butter and marshmallow fluff until combined, about 1 minute. Beat in the vanilla and gradually begin adding in the confectioners' sugar, about one cup at a time, until frosting is light and fluffy. If frosting is too thick, add in a little of the milk or heavy cream to thin it out. You want the frosting to be spreadable, so not too thick.
Spread the frosting onto the cooled cake in an even layer. Sprinkle with toffee bits and serve. Store leftovers either in the fridge or at room temperature, but covered either way.