Heat oven to 400°F. Line a rimmed baking sheet with parchment paper.
Make the biscuits: In a large bowl, whisk together flour, brown sugar, baking powder, 1 teaspoon salt and baking soda. Use a pastry blender or fingers to cut 6 tablespoons cold butter into flour mixture until mixture resembles coarse crumbs.
In a separate medium bowl, whisk together mashed sweet potato and cold buttermilk. Use a rubber spatula to stir sweet potato mixture into flour mixture until nearly combined.
Turn dough onto a lightly floured surface; gently shape dough into a cohesive ball. Gently pat dough into a 1-inch-tall square. Using a sharp knife or bench scraper, cut dough into 9 equal pieces (3 rows by 3 rows). Place dough squares on parchment paper-lined baking sheet spaced at least 2 inches apart. Bake biscuits 15 to 18 minutes or until lightly browned and baked through.
Meanwhile, make the marshmallow icing: In a large bowl, whisk together 3/4 cup powdered sugar, vanilla and pinch salt. In a small saucepan over medium heat, heat 1 1/2 tablespoons butter and water until butter is melted. Add marshmallows; stir 1 to 2 minutes until melted and smooth.
Stir marshmallow mixture into powdered sugar mixture, whisking until a smooth but thick glaze forms. Add just enough remaining 1/2 cup powdered sugar until icing is very thick but smooth and spreadable.
Spoon, spread or drizzle marshmallow icing on top of warm biscuits, about 1 tablespoon per biscuit. Serve immediately.