Combine yeast, 1 teaspoon of sugar, and lukewarm water. Allow this to proof for approximately 5 minutes, it will smell yeasty and a nice foam develops.
In the bowl of a stand mixer, with beater blade attached, add 2 cups hot water, butter, salt, and sugar and beat until combined, around 30-40 seconds. Allow to cool to room temp, usually, this happens quickly.
Stir in 2 cups of flour, and stir until combined. Add eggs and yeast mixture, stirring to incorporate well.
Replace the beater blade with the dough hook, and begin adding the flour 1-2 cups at a time until the dough forms a ball, around 2-3 minutes.
Place dough on a well-floured surface, and begin kneading, adding flour (up to 10 cups) until no longer sticky and the dough feels satiny and smooth.
Oil the inside of a medium to large bowl, place the dough into the bowl, and flip over once so the dough is coated with oil. Cover with a plastic shower cap or a damp tea towel and let rise in a warm place for approximately 45 minutes, or until the dough has doubled. You can use the finger poke trick, if you poke the dough and the indent remains your dough is ready.
On a lightly floured surface, place dough, divide in half, and set one half aside. Roll one half in a rectangle, about 22x12 inches. Combine very soft butter, brown sugar, and cinnamon in a bowl, divide in two, and spread on the rectangle.
Roll the rectangle into a long roll, 22 inches long. Use a knife, bench cutter, or string/dental floss to cut the dough into 12 even portions. Place in a greased baking pan, leaving 1-2 inches between rolls. Repeat with the other half of the dough.
Cover the pans with a shower cap or tea towel, and allow the rolls to rise a second time until they are doubled.
Preheat your oven to 350 °F. Once the rolls have doubled in size, bake them for 20-30 minutes or until they turn golden brown. Please note that the outer edges of the rolls will cook faster, leaving the middle portion doughy. This is my preference, but not everyone may like it that way. If you want your rolls to be fully cooked, leave them in the oven for a little longer.
Allow to cool in the pan. While cooling go ahead and make the frosting by combining the butter, sugar, milk, and vanilla using a whisk. While the rolls are still warm spread the desired amount over the top and watch as it melts into your cinnamon rolls.
These are best enjoyed warm, so eat up! If you are making them ahead they do warm up nicely if you place one roll in the microwave for 30-40 seconds.