In a large bowl (to allow for about 7-8 cups of dough to double in bulk), whisk together the flour, yeast, sugar and salt. Make a well in the center of the dry ingredients.
In a 2-cup liquid measuring cup, whisk together the eggs and pour them into the well. Use the same measuring cup for the hot water. Pour it around the edges of the well (not directly on the eggs) and then add the melted butter to the bowl. Use a large spoon to mix the ingredients together until a soft, rather wet dough is formed. It won't look like traditional cinnamon roll dough; it will be much softer and it's ok if it looks a bit lumpy. Magic happens overnight, I promise.
Cover the bowl with greased plastic wrap and refrigerate overnight or for 8-10 hours.
Using about 1/4 - 1/3 cup flour (more or less), dust a clean countertop. Lightly punch down the chilled dough and roll it out on the floured counter to a long, skinny rectangle (about 24-inches long and 7 or 8-inches wide).
Spread the 4 tablespoons melted butter on the rectangle. It will solidify and be easier to work with as you spread it on the chilly rectangle of dough. Combine the sugar and cinnamon and spread it on top of the butter, lightly pressing it in.
Fold one long edge of the rectangle up to meet the other long edge so the dough is folded in half. Use a pizza cutter or knife and cut the dough into 1-inch strips. With each strip, hold an end in each hand and twist it up several times and roll it around the center into a circle (see pictures below for a visual). Place on a large, rimmed baking sheet (11X17-inch) lined with parchment paper (about 12 per tray).
Cover the trays with greased, plastic wrap and let the rolls rise until puffy and doubled, an hour or so.
Bake at 375 degrees F for 12-14 minutes until just barely golden on top (don't overbake or they'll be dry).
For the glaze, whisk together the powdered sugar, butter, milk, and vanilla. Add more milk as needed until the glaze is thick but pourable. Let the rolls cool for 5 or so minutes before drizzling with glaze.
Notes
Make Ahead: if you want to have these ready even faster on a given morning, simply start a day ahead of time. Make the dough the morning before, refrigerate it for 8-10 hours, take out and follow the directions to shape and place on the baking sheet. Cover the shaped rolls with greased plastic wrap and refrigerate until the next morning. Take out in time to come to room temp and rise and then bake as directed.