Make the caramel base:
In a medium saucepan over medium heat, combine the butter, brown sugar, heavy cream, maple syrup, and salt. Stir constantly until the butter melts and the sugar dissolves, about 3-4 minutes. Let it bubble for another minute, then remove from heat. Pour the caramel into a 9x13-inch baking pan and scatter the pecans or walnuts evenly over the top. Set aside.
Make the filling:
In a small bowl, mix together the very soft butter, brown sugar, cinnamon, and cornstarch with a fork until it forms a spreadable paste.
Roll out the dough:
Lightly flour your work surface. Turn out the cold dough and press it gently into a rectangle. Using a rolling pin, roll the dough into a large rectangle, approximately 16 inches wide by 12 inches tall, about 1/4 inch thick.
Spread the cinnamon filling evenly over the entire surface of the dough, leaving a 1-inch strip bare along the top long edge.
Starting from the long edge closest to you, roll the dough into a tight log. When you reach the bare edge, pinch it gently to seal the seam.
Position the log seam-side down. Using a sharp knife or bench scraper, cut the log into 12 equal pieces.
Place the 12 rolls cut-side up in the prepared pan with the caramel and nuts. They should be relatively close together but not completely squished.
Cover the pan with a damp tea towel or plastic wrap and let proof at room temperature for 1-2 hours, until the buns are puffy and nearly touching each other. When you press a finger gently into the side of one, the indentation should fill back slowly but not completely.
Meanwhile, preheat your oven to 350°F (175°C).
Once proofed, bake the sticky buns for 28-35 minutes, until they are deep golden brown on top. The internal temperature should be around 190°F if using an instant-read thermometer.
As soon as the buns come out of the oven, let them sit for exactly 5 minutes. Set a timer.
After 5 minutes, place your serving platter or sheet pan over the top of the baking pan. Using oven mitts, hold both pans together and flip the whole thing over confidently and quickly. The sticky buns should release onto the platter with all the caramel and nuts on top.
Let the buns cool for about 10 minutes before serving. They are best when still slightly warm, with the caramel gooey and the interior soft and steamy.