Melt ½ cup (1 stick) butter and set aside to cool.
Add yeast and 1 Tablespoon of sugar to warm water in mixer bowl. Let stand 5 to 10 minutes to allow the yeast to proof. Mixture will become foamy.
In a medium bowl, blend together 3 tablespoons sugar, 3 cups of flour and 2 teaspoons salt.
Once yeast has proofed, blend in eggs, butter and flour mixture using low speed of mixer.
Attach dough hook to mixer and gradually add remaining flour until dough clings to hook and cleans the sides of the bowl. Continue mixing on low speed for a couple of minutes to knead the dough until it is smooth and elastic. (If using a mixer without a dough hook, remove dough to a floured surface and then knead and mix in flour.) Dough will be slightly sticky to the touch.
Use a spatula to round the surface of the dough in the mixing bowl. Cover the bowl and allow the dough to rise in a warm spot until doubled in size, about 1 to 1½ hours.
Punch dough down and let stand 15 minutes.
Line 2 large baking sheets with parchment paper.
Combine sugars, cinnamon and salt in a small bowl.
On a lightly floured surface, roll and stretch dough into a 24×9-inch rectangle. Spread with softened butter and sprinkle evenly with sugar mixture. Tightly roll up dough jelly-roll fashion starting at the long side to form a log and pressing edge to seal.
Cut log into 24 slices starting in the middle of the rolled log and dividing segments twice and cutting final segments into thirds; this will help keep slices more evenly sized as the dough expands.
Place slices about 2 inches apart on prepared baking sheet. Cover and let rise in a warm place, free from draft, until doubled in size – about 1 hour.
Preheat oven to 350˚F.
Bake cinnamon rolls until lightly browned, 15 to 20 mins. Let the rolls cool on the parchment lined pans on which they were baked; this allows most of the cinnamon filling to remain with the rolls.