In a large mixing bowl, combine the all-purpose flour, instant yeast, granulated sugar, and salt. Whisk together until evenly blended.
In a separate bowl, whisk together the melted butter, warmed milk, eggs, and vanilla extract until fully combined and smooth.
Gradually pour the wet mixture into the dry ingredients, stirring with a wooden spoon or spatula until the dough begins to form and come together.
Transfer the dough to a floured surface and knead for 5-7 minutes, or until the dough feels smooth and elastic. Once kneaded, place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm environment for approximately 1 hour, or until it has doubled in volume.
While the dough is rising, prepare the filling. In a small bowl, combine the packed brown sugar, ground cinnamon, and chopped pecans. Mix until evenly distributed and set aside.
After the dough has risen, gently punch it down to release the air. Transfer it back to a floured surface and roll it out into a rectangle approximately ¼ inch thick.
Evenly spread the softened butter across the surface of the rolled-out dough, then generously sprinkle the brown sugar filling mixture on top, ensuring an even distribution.
Starting from one long edge, roll the dough tightly into a log shape. With a sharp knife, cut the log into 12 equal pieces, creating your sticky buns.
For the sticky topping, in a medium mixing bowl, whisk together the melted butter and maple syrup until combined. Pour this mixture into the bottom of a greased 9x13 inch baking dish. Sprinkle the chopped pecans evenly over the syrup.
Place the cut sticky buns cut-side down on top of the pecan mixture in the dish. Cover the dish with plastic wrap and allow it to rise for an additional 30 minutes.
Preheat your oven to 350°F (175°C). Once the buns have completed their second rise, bake them in the preheated oven for 25-30 minutes, or until they are golden brown and smell delicious.
Remove the baking dish from the oven and allow the buns to cool for about 5 minutes. Then, carefully invert the dish onto a serving plate to unveil the gooey sticky topping.