Makes 14 buns

Divide dough in half; keep one half covered and chilled while working with the other. On a floured work surface, roll dough into a 11 inch wide, 13 inch long, and 1/4 inch thick rectangle. Dot surface evenly with half the softened butter and fold dough in thirds. Turn it so the closed fold is on the left and roll out again, without rolling over the edges. Fold dough in thirds again, wrap in plastic, and refrigerate 30 minutes. Repeat rolling, folding, and chilling with second piece of dough and remaining butter.

Mix sugar and cinnamon together; set aside. Remove first piece of dough from refrigerator and roll into an 11 inch wide, 13 inch long, and 1/4 inch thick rectangle. Paint surface with beaten egg. Leaving top quarter of dough bare, sprinkle half the cinnamon sugar and half the chopped pecans; spread with fingers to distribute evenly. Starting from the short side, roll into a log.

Wrap in plastic and freeze until firm. Repeat with second piece of dough. While logs are chilling, prepare pans by pressing a stick of butter evenly over the bottom of each 9-inch round pan; sprinkle brown sugar evenly over butter. Remove a log from freezer and trim ends if ragged. Slice log into seven 1 1/2-inch slices with a serrated knife. Lay each slice flat, flatten slightly, and round the sides. Press 3 pecans, flat side up into each slice. Turn slices over carefully into pan, placing buns in a circle with the last one in the center; seams of buns should face outside of pan.

Repeat with second log. Let rest, uncovered, for 2 hours, until slices touch. Arrange oven racks so one rack is in the middle and the other just below, and preheat to 350°F. Put pans on middle rack and put a foil-lined jelly-roll pan underneath to catch drips. Bake 35 to 40 minutes, until golden brown. Invert immediately on serving dish.