01 - In a large bowl, blend lukewarm milk and active dry yeast. Allow to rest for 5 minutes until foamy, then combine with granulated sugar, egg, and melted butter. Incorporate flour and salt, mixing to achieve a cohesive dough. Knead the dough on a well-floured surface for 8 to 10 minutes, or utilize a stand mixer with a dough hook, until the dough is smooth and elastic. Transfer to a lightly greased bowl, cover, and let rise in a warm environment for 1 to 1.5 hours or until doubled in volume.
02 - In a small saucepan set over medium heat, melt butter and incorporate maple syrup, packed brown sugar, and salt. Simmer gently for 2 minutes without boiling. Pour the mixture into a greased 9x13-inch baking pan and distribute the toasted pecan halves evenly across the surface.
03 - Combine packed brown sugar and ground cinnamon in a small bowl. Set aside for assembly.
04 - Punch down the risen dough and roll it out on a floured surface to form a 16x12-inch rectangle. Evenly spread the softened butter over the dough, then sprinkle the cinnamon-sugar mixture across the entire surface. Starting from one long edge, tightly roll the dough into a log. Trim the edges if needed, then slice into 12 uniform pieces.
05 - Position the sliced buns cut-side up atop the maple-pecan topping in the prepared pan. Cover with a cloth and allow a second rise for 30 to 40 minutes, until the buns appear puffy.
06 - Bake in a preheated oven at 350°F for 30 to 35 minutes, until the buns are golden brown and cooked through. If excessive browning occurs, tent with aluminum foil. Cool in the pan for 5 minutes, then invert the buns carefully onto a serving platter, ensuring the sticky pecan topping coats each bun. Serve warm.