Preheat oven to 425°F and line a baking sheet with parchment. In a bowl, whisk flour, sugar, baking powder, and salt. Cut in cold butter until pea-sized crumbs form. Stir in buttermilk until dough just comes together.

On a floured surface, pat dough into a 10×14-inch rectangle. Spread softened butter over the dough, leaving a bare border on one long side. Mix brown sugar and cinnamon, then sprinkle evenly over the butter and press lightly.

Roll up tightly from the long side opposite the border. Pinch the seam. With a serrated knife, saw the log into 8 rounds. Place cut side down on the sheet.

Brush tops with extra buttermilk. Bake 12 to 15 minutes until deep golden. Cool on the pan 5 minutes.

Whisk powdered sugar, 1 tbsp milk, and vanilla. Thin with more milk as needed. Drizzle over warm biscuits and serve.