In a small bowl, combine warm water, yeast and 2 tablespoons sugar; let stand for 5 minutes.
In a medium bowl, combine flour, remaining 2 tablespoons sugar and salt, whisking to blend.
In the bowl of a stand mixer fitted with a paddle, combine yeast mixture, 4 tablespoons melted and cooled butter, milk, egg and vanilla.
Gradually add flour mixture to yeast mixture, beating until smooth after each addition. Turn dough out onto a lightly floured work surface; knead until smooth and elastic, about 3 to 5 minutes. Place dough in a lightly greased bowl, turning to coat the top. Cover with greased plastic wrap or a dishtowel, and let stand at room temperature until the dough has doubled in size, 1 to 1½ hours.
Lightly spray a 10- to 12-inch cast-iron skillet with melted butter and set aside. In a small bowl, combine brown sugar and cinnamon.
Punch dough to release any excess air. Turn dough out onto a lightly floured surface and roll to a large rectangle, roughly 18 by 10 inches. Brush dough generously with melted butter and sprinkle with the brown sugar mixture, leaving a 1-inch border on one of the long sides of the dough. Starting on the long side, tightly roll up the dough, towards the clean border, into a log, pressing edge to seal. Cut into 12 rolls.
Place rolls cut side down in the prepared skillet. Cover, and let rise at room temperature until doubled in size, approximately 1 hour. Preheat oven to 350°.
Bake cinnamon rolls until lightly browned, 25 to 30 minutes. To make the glaze, whisk together confectioners’ sugar, butter, milk and vanilla in a bowl until smooth. Drizzle over warm rolls.