Measure the brown sugar, baking soda, salt, vanilla, and egg into a mixing bowl.
Add the buttermilk, then the flour; stir until thoroughly combined into a dough.
Turn the dough out onto a lightly floured surface and knead for 2 minutes.
Roll the dough into a 12x24 inch rectangle and spread with the melted butter.
Sprinkle with the brown sugar and cinnamon.
Roll the dough into a log beginning with the wide side. Stretch slightly.
Cut into two-inch pieces and put these pieces into greased muffin tins or cupcake liners.
Bake at 375°F for 20 minutes or until golden brown.
Allow to cool for 5 minutes in the muffin tin, then transfer to a wire rack.
Make the icing: combine the powdered sugar, milk or cream, and vanilla (optional) in a small bowl until it forms an icing consistency. If too thin, add more powdered sugar; if too thick, add more milk/cream.
Drizzle the icing over the tops of the muffins decoratively.