Warm the milk to about 110°F, pour into the stand mixer bowl, and sprinkle the yeast and a pinch of sugar over the top. Let sit 5 to 10 minutes until foamy.
Add the remaining sugar, melted butter, and eggs, then whisk gently. Attach the dough hook, add flour and salt, and mix on low until a shaggy dough forms.
Knead for 6 to 8 minutes until smooth, elastic, and pulling away from the bowl. The dough should feel slightly tacky, not sticky.
Shape the dough into a ball, place in a lightly greased bowl, cover, and let rise in a warm, draft-free spot for about 1 hour, until doubled in size.
Melt the butter, brown sugar, maple syrup, and salt in a small saucepan over medium heat. Stir until smooth, remove from heat, and stir in the heavy cream.
Pour the caramel evenly into a prepared 9x13 inch pan and scatter the chopped pecans over the top in an even layer. Set aside.
Punch down the risen dough, turn out onto a lightly floured surface, and roll into a large rectangle, roughly 16 by 12 inches.
Spread softened butter evenly over the dough, then sprinkle the brown sugar, cinnamon, and a pinch of salt on top, pressing gently so it sticks.
Starting from the long edge, roll the dough tightly into a log. Slice into 12 even rolls using a sharp serrated knife or unflavored dental floss.
Arrange the rolls cut side up on top of the caramel and pecans in the pan, leaving a little space between each one for the second rise.
Cover the pan loosely with plastic wrap or a towel and let the rolls rise in a warm spot for 30 to 45 minutes, until puffy and touching. Alternatively, refrigerate overnight and bake fresh in the morning.
Preheat oven to 350°F. Bake for 25 to 30 minutes, until the tops are golden brown and the caramel is bubbling at the edges. Tent with foil if browning too quickly.
Remove from the oven and rest for 5 minutes, no longer. Place a large serving platter over the pan and carefully invert it. Let the pan sit inverted for a minute before lifting away, then scrape any extra caramel and pecans onto the buns. Serve warm.