Using a standing electric mixer, combine 5 cups flour, the sugar, yeast and table salt. Add the softened butter gradually and mix on low speed to combine. Mix in 1 egg on low speed.
With the machine on, add the lukewarm water in a slow, steady stream (the dough will be very wet). Increase the speed to medium and mix for 2 minutes. Mix in 3/4 cup flour on low speed, then increase the speed to medium and mix until a ball forms, about 1 minute.
Attach the dough hook to the mixer and knead the dough for 10 minutes, adding more flour if necessary, until smooth, elastic and not sticky to the touch. Shape into a ball, transfer to a greased bowl, cover and let rise until doubled in size, 30 to 45 minutes. Punch down the dough, knead lightly, cover again and let rest for 15 minutes.
Position a rack in the middle of the oven and preheat to 350 degrees . Generously brush the bottom and sides of two 9-inch round cake pans with some of the melted butter. Pour the remaining melted butter into another cake pan or a wide, shallow dish. Roll out the dough into a 14-by-16-inch sheet. Using a 2 1/2-inch biscuit cutter, cut out 40 rounds, gathering the scraps and rolling out as necessary.
Dip both sides of 20 dough rounds into the melted butter; fold in half, lining up the buns seam side down against each other in 2 rows of 7 each. Tuck 3 more folded rounds on each long side of the rows to fill the pan. Cover and let rise until doubled in size, 30 to 45 minutes. (Repeat with the remaining 20 dough rounds in the second cake pan, cover with plastic wrap and refrigerate for the Cinnamon Sweet Rolls (recipe also in Recipe Finder).
While the dough is rising, mix together the seeds and coarse salt; set aside.
Beat the remaining egg with 1 teaspoon of water. Brush the risen dough with the egg wash and sprinkle evenly with the seed mixture. Bake until the rolls are browned and a toothpick inserted into the center comes out clean, about 30 minutes. Let cool on a rack; serve warm or at room temperature.