• Before you begin: Bring your eggs and butter to room temperature and warm the milk to 90º F. Have two 9" round cake pans ready, and set a sheet pan on the rack below where the buns will bake to catch any drips. Preheat the oven to 350º F while the buns are on their second rise.

For the dough

• Place the warm milk, yeast, and half of the flour into the bowl of your stand mixer with the dough hook attached and mix until combined.
• Add in the softened butter, sugar, salt, eggs, and the rest of the flour and mix until combined.
• Add the corn syrup (if using) and mix until fully combined.
• Increase the speed to medium. Continue mixing for 10 to 20 minutes, or until the dough begins to clean the sides of the bowl and forms a smooth ball. This is a very soft dough, so don't worry if it seems like a sticky mess at first, just keep mixing.
• Pull off a small piece of dough and gently stretch it between your fingers. It should stretch thin enough to be nearly translucent without tearing. If it tears or still feels sticky, keep mixing.
• Shape the dough into a smooth ball and place it into a greased bowl. Cover with a tea towel and let rise for 90 minutes in a warm place. To create a reliably warm proofing environment, preheat your oven to 170º F for 5 minutes, then turn it off. Place a bowl of warm water in the back of the oven, put the covered dough inside, and shut the door.

For the caramel glaze

• Add the softened butter, granulated sugar, brown sugar, cinnamon, and salt to a large bowl and mix with a whisk or electric mixer until light and fluffy. Drizzle in the corn syrup and vanilla and mix until combined. Use less corn syrup if you want a thicker, firmer caramel.
• Divide the glaze between the two pans, spreading it over the bottoms and sides, and sprinkle the pecans evenly over the top. This layer flips over after baking and becomes the gooey top of the sticky buns.

To shape the buns

• Once your dough has doubled, divide it in half. Roll each half out on a lightly floured surface into a rectangle about 15 inches wide, 12 inches tall, and ½ inch thick. If the dough keeps springing back, cover it and let it rest for 5 minutes.
• Mix the butter, sugar, and cinnamon for the filling until smooth. Spread half of it over each rectangle in an even layer, leaving about 1 inch bare along one long edge, then sprinkle the pecans evenly over the filling.
• Starting from the long edge with filling, roll each rectangle up into a snug log (not too tight, or the centers pop up into cones as they bake). Brush a little water on the bare edge and press to seal.
• Use a ruler to mark each log into 8 equal pieces and cut them with a serrated knife. Dental floss won't work here because it can't cut through the pecans.
• Place 8 buns cut side down on top of the glaze in each pan, one in the middle and seven around it. Cover with a tea towel and let them rise in a warm place for about 90 minutes, until they're puffy and slightly touching each other. That's how you know they've risen enough. To bake them the next morning, cover the pans tightly with plastic wrap and refrigerate them for up to 16 hours, then let the buns rise in a warm spot until puffy, about 1.5 to 2 hours, before baking.

To bake

• Bake at 350º F for 25 to 30 minutes, until a thermometer in the center bun reads 195º to 200º F. If the tops brown too quickly before the center is done, lay a piece of foil loosely over the pans. Refrigerated buns may need a few extra minutes.
• Let the buns cool in the pans for 5 minutes. Place a large serving plate on top of one pan, hold them together firmly with oven mitts, and flip in one quick motion. Lift the pan away slowly. Repeat with the second pan.
• Scrape any caramel left in the pans over the buns. If some of it has set, put the pans back in the oven for 5 minutes to loosen it, then drizzle it on top. Serve warm.