Combine the sugar and the lemon zest in a bowl and rub it together with your fingers until the zest is interspersed through the sugar.

Beat the mixture for 2 minutes, scraping down the sides of the bowl as needed. Add 1 more cup of flour, then beat another 2 minutes on high, scraping the bowl occasionally. Add in just enough of the remaining flour so that the dough will form into a ball.

Lightly flour a work surface, then knead the dough until it is smooth and elastic and it springs back when lightly touched with 2 fingers, 6 to 8 minutes. Cover with a towel and let the dough sit for 10 minutes.

Spray a 9 x 5-inch loaf pan with nonstick cooking spray.

For the filling, combine the sugar and the lemon zest and rub it together with your fingers until the zest is interspersed through the sugar. Measure out 1/4 cup of the mixture and set aside.

Roll the dough into a long rectangle, 7 x 24-inches long. Spread the 2 tablespoons of soft butter evenly over the surface of the dough. Sprinkle the reserved 1/4 cup of sugar evenly over the butter. Beginning at the long end of the rectangle, roll it up tightly. Pinch the seams to seal. Cut the dough into 24 equal slices. Dip each slice into the melted butter, then into the remaining lemon sugar mixture. Place the slices in the prepared loaf pan.

Cover the pan with a towel and let it sit in a warm, draft-free area until doubled in size, about 45-60 minutes.

Preheat the oven to 350ºF. Bake the loaf until the bread is golden brown, 25-35 minutes. Cool on a wire rack for 10 minutes, then invert onto a serving plate.

In a bowl, beat the powdered sugar, butter, milk, lemon juice and lemon zest together until smooth and creamy. Drizzle the icing over the warm loaf.