Prep the Yeast Mixture: Preheat the oven on the lowest heat setting (usually 170°F / 77°C), then turn it off to create a warm proofing environment. In a heatproof bowl, melt the cold cubed butter, brown sugar, vanilla extract, salt, and milk in the microwave for 1 minute. Stir, then heat for another 30 seconds. Stir until the butter melts and the sugar dissolves. Ensure the mixture is warm, between 105°F – 115°F (41°C – 46°C).
Knead the Dough: In a stand mixer bowl fitted with a paddle attachment, add 3 cups of all-purpose flour. Pour in the warm butter/milk mixture and the yeast. Mix on low speed until combined. Incorporate the room-temperature eggs one at a time, scraping down the bowl. Switch to a dough hook, add the remaining all-purpose flour, and knead the dough for 10 to 15 minutes until it is smooth and no longer sticky. (Note: If your mixer is too small, knead by hand).
The First Rise: Add 1 Tablespoon of vegetable oil to a large bowl. Shape the dough into a tight ball, roll it in the oil to coat, and loosely cover the bowl with plastic wrap and a clean towel. Place the bowl inside the turned-off, warm oven for 1 to 1 ½ hours. Do not open the door!
Roll and Fill: Punch down the risen dough and transfer it to a floured counter. Roll it into a rectangle measuring 26 inches wide by 20 inches long (1 cm thick). Melt 1 cup of cold butter in the microwave for 30 seconds and mix in the brown sugar, cinnamon, and salt. Spread this filling evenly onto the dough, leaving a clean 2-inch gap along the bottom edge. Roll the dough tightly toward you into a log. Cut the log in half and brush the outsides with melted butter.
The Thread Trick: Lightly score the dough logs with a knife to mark 15 equal sections. Slide a long piece of clean sewing thread underneath the log, cross the ends over the top, and pull tight to slice perfectly clean rolls. Brush the insides of two 9x13-inch baking dishes with melted butter. Place the rolls cut-side up inside the dishes.
Second Rise and Bake: Place the baking dishes back into the warmed oven for another 30 minutes to 1 hour to allow the rolls to double in volume. Remove from the oven. Preheat the oven to 350°F (177°C). Bake each pan on the middle rack for 25 to 35 minutes, or until golden brown.
Glaze: In a medium bowl, whisk together the powdered sugar, heavy cream, and vanilla. Let the baked cinnamon rolls cool for 15 minutes, then glaze each roll with 2 to 3 Tablespoons of icing. Serve warm!