In a small bowl, combine the warmed milk, granulated sugar, and active dry yeast. Let it sit for about 5-10 minutes, until frothy.
In a large mixing bowl, combine the activated yeast mixture, melted butter, eggs, and vanilla extract. Stir well. Gradually add the flour and salt, mixing until the dough begins to form.
Transfer the dough onto a floured surface and knead for about 5-7 minutes until smooth and elastic. Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.
In a small bowl, mix together the brown sugar and ground cinnamon. Set aside.
Once the dough has risen, punch it down and roll it out on a lightly floured surface into a rectangle (about 16x12 inches).
Spread the cinnamon-sugar mixture evenly over the dough. Sprinkle the chopped pecans generously on top, pressing them down slightly.
Carefully roll the dough tightly from one long edge to the other to form a log. Cut the log into 12 equal pieces.
Grease a 9x13 inch baking dish with butter. Drizzle half of the caramel sauce on the bottom, then arrange the cinnamon rolls in the dish.
Cover the rolls with a clean cloth and let them rise for another 30 minutes.
Preheat your oven to 350°F (175°C).
Bake the cinnamon rolls for 25-30 minutes, until golden brown. While baking, heat the remaining caramel sauce for drizzling.
Once baked, remove from the oven, allow to cool slightly, and then drizzle the warm caramel sauce over the top. Serve warm.