Begin by combining the warm milk and yeast in a large bowl, allowing it to sit for 5 minutes until foamy and activated. Add the melted butter, sugar, eggs, and vanilla, whisking until well combined.
Gradually incorporate the flour and salt, mixing until a soft dough forms. Stop adding flour when the dough feels slightly sticky but pulls away from the sides of the bowl.
Turn the dough onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. The dough should spring back when lightly pressed with your fingertip.
Place the dough in a greased bowl, cover with plastic wrap or a damp cloth, and let rise in a warm location for about 1 hour, or until doubled in size.
While the dough rises, make the sticky topping by combining the maple syrup, brown sugar, butter, and salt in a saucepan over medium heat. Stir consistently until the mixture comes to a gentle boil, then simmer for 2 minutes until slightly thickened.
Remove from heat, stir in the vanilla extract, and pour into a greased 9×13-inch baking pan. Arrange the pecan halves decoratively on top of the syrup mixture.
Mix the brown sugar, cinnamon, and nutmeg in a small bowl for the filling. After the dough has doubled, punch it down and roll it out on a lightly floured surface to a 16×20-inch rectangle.
Spread the softened butter evenly across the surface, leaving a 1/2-inch border along one long edge. Sprinkle the cinnamon-sugar mixture over the butter, followed by the chopped pecans, pressing lightly to adhere.
Starting from the long edge without the border, tightly roll the dough into a log, pinching the seam to seal.
Using a sharp knife or unflavored dental floss, cut the log into 12 equal pieces, each about 1.5 inches thick. Arrange the rolls cut-side up on top of the prepared maple-pecan mixture in the baking pan.
Cover with plastic wrap and let rise for 30-45 minutes, or until noticeably puffy. During this second rise, preheat your oven to 350°F.
Bake the rolls for 25-30 minutes, or until golden brown and the internal temperature reaches 190°F. Tent with aluminum foil after 15 minutes if the tops are browning too quickly.
Once baked, allow the rolls to cool in the pan for exactly 5 minutes.
Place a large serving platter or baking sheet over the pan and carefully flip to invert the rolls. Allow the sticky maple glaze to drip down the sides for a minute before removing the baking pan. Serve warm.