In the bowl of a stand mixer, combine warm milk, yeast, and 1 tablespoon of the granulated sugar. Let stand for 5-7 minutes until foamy and active.
Add remaining granulated sugar, melted butter, eggs, 2 cups of flour, and salt to the yeast mixture. Mix with the paddle attachment on low speed until combined, then switch to the dough hook. Gradually add remaining flour 1/2 cup at a time, kneading on medium speed for 6-8 minutes until the dough is smooth, elastic, and slightly tacky.
Transfer dough to a greased bowl, cover with a damp towel, and let rise in a warm place for 1-1.5 hours until doubled in size.
While dough rises, make the caramel layer. In a small saucepan over medium heat, melt 1/2 cup butter with 1 cup brown sugar and heavy cream, stirring constantly. Bring to a gentle boil for 1 minute, then remove from heat and stir in vanilla. Pour evenly into a greased 9x13-inch baking pan and sprinkle toasted pecans over the caramel.
Once dough has doubled, punch it down and turn out onto a lightly floured surface. Roll into a 16x12-inch rectangle with even thickness throughout.
Spread the softened butter over the entire surface of the dough, leaving a 1/2-inch border on one long edge. Mix the 3/4 cup brown sugar with cinnamon and sprinkle evenly over the butter.
Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam to seal. Using unflavored dental floss or a sharp knife, cut into 12 equal slices, each about 1 1/3 inches thick.
Place rolls cut-side down over the caramel and pecans in the prepared pan, spacing them slightly apart. Cover loosely with plastic wrap and let rise for 30-45 minutes until puffy (or refrigerate overnight and let sit at room temperature for 30 minutes before baking).
Preheat oven to 350°F. Bake rolls on the center rack for 25-28 minutes until golden brown and the internal temperature reaches 190°F. The caramel will be bubbling around the edges.
Remove from oven and immediately run a knife around the edges of the pan. Let cool for exactly 5 minutes, then carefully invert onto a large serving platter or baking sheet. Scrape any remaining caramel from the pan over the rolls. Serve warm.