Open crescent roll dough and carefully unroll each piece (refer to images above). Working with one piece at a time lay out and bring four triangles together on lightly greased work surface. Pinch portions and perforated seems together. Carefully turn dough over and repeat on opposite side.
Roll sealed dough out to about a 7 by 7-inch square. Brush with 1 Tbsp butter. Sprinkle with brown sugar, spread out even. Sprinkle evenly with 1 tsp cinnamon.
Start on one end and roll dough fairly snug to opposite end to create a log shape. Cut (side to side, not just pressing down, using a sharp knife) into portions.
Transfer to a well greased mini muffin tin. Repeat process with remaining crescent roll dough, butter, brown sugar and cinnamon.
Bake in preheated oven until just golden brown, about 9 - 11 minutes. Let cool just a minute or two, run knife around edges while still warm and transfer to a wire rack set over paper towels.
For the icing: in a mixing bowl whisk together powered sugar, milk and vanilla extract.
Transfer to a small resealable bag an cut a small corner or just use a spoon, drizzle over tops. These are best served warm but if you have leftover just store in an airtight container.