Add the sugar, salt, eggs and 1 cup of flour to the bowl with the yeast mixture. Using a dough hook, run the heavy duty mixer on low speed for about a minute until the mixture is just about incorporated. Add the remaining half cup of flour and run the mixer in medium speed. Continue to beat, scraping the bowl as needed, for about 15-20 minutes. You will know when the dough is ready if it is coming together in the center of the bowl, and also attaching itself into the dough hook. You should see the dough slapping the sides of the bowl, like it is almost violently throwing itself to the sides white it still clinging and rotating with the dough hook. You should also hear the slapping sounds.
Now add the butter bit by bit. Make sure that the butter is in in room temperature, but not warm or oily. When you add the butter, the dough will fall apart again for a moment. Continue to beat until you hear the slapping sounds again. This should take about 5 minutes or so. The dough is now , once again, clinging together in the center and in the dough hook with the slapping sound. Dough is sticky but shiny at this point.
Place the ball of dough into a greased bowl and cover with a plastic wrap. Let stand in room temperature until the size is doubled, about 2 hours.
After the dough has doubled in size, gently deflate it by lifting and then letting it fall back to the bowl. Cover the bowl again with a plastic wrap and chill in the refrigerator for 6 hours or overnight. The dough will double in size again ( After the long chill, you can now divide the dough in half. You are only going to use 1/2 of the dough for one bread ring. Reserve the other half for future use. You can freeze the dough for up to three weeks, tightly wrapped in plastic and foil).