In a medium bowl, whisk together 2 cups flour, salt, 1 teaspoon granulated sugar, and instant yeast. Add the water. Using a rubber spatula, mix until the liquid is absorbed and the ingredients form a sticky dough ball. Cover the bowl with a damp tea towel or plastic wrap and set aside in a warm spot to rise for 1 to 1 ½ hours, until the dough has doubled in bulk.
Set a rack in the middle of the oven and preheat it to 375°F. Grease an 8-or 9-inch cast-iron skillet or circular or square baking pan with the softened butter. In a small bowl, stir together the cinnamon and remaining ¼ cup granulated sugar. Sprinkle 1 tablespoon of the mixture over the bottom of the prepared skillet.
Spread ¼ cup flour over a clean surface. Using two forks, deflate the dough by releasing it from the sides of the bowl and pulling it toward the center. Rotate the bowl quarter turns as you deflate, turning the mass into a rough ball. Use the forks to lift the dough onto the prepared clean surface. Using as much flour as necessary from the surface, dust your hands and the exterior of the dough, then shape the mass as best you can into the ball. Using a bench scraper or a knife, divide the mass into twelve to fourteen equal-size pieces, each 1 to 2 inches in diameter.
Using as much flour as needed to prevent sticking, shape each piece into a rough ball and immediately transfer them into the greased pan, evenly spaced. Let rise for 20 to 25 minutes. The balls may not rise to fill the skillet entirely, but they will puff when they bake.
Brush each ball with some melted butter, then pour over the remainder. Sprinkle with the remaining cinnamon-sugar mixture. Transfer the skillet to the oven and bake for 20 to 25 minutes, until golden.
Meanwhile, make the glaze: Whisk together the confectioners’ sugar and milk in a small bowl until it reaches a pourable consistency, adding more milk as needed. Remove the bread from the oven and let it cool for 5 minutes in the pan before inverting the pan onto a plate, then invert it again onto a serving platter. Drizzle with glaze. Serve immediately.