Proof the yeast. In a stand bowl, or a large bowl, stir together the milk, yeast and 1 teaspoon sugar. Let sit for 5 to 10 minutes until bubbly and foamy.
Make the dough. In a bowl of your stand mixer with a paddle attachment, add the remaining ingredients - flour, salt, remaining sugar, eggs, and butter - until a shaggy dough forms.
Knead the dough. Fit the mixer with a dough hook attachment, and knead at medium speed for 6-8 minutes. If the dough is super sticky, add additional flour a little at a time if needed. If you are kneading the dough by hand, then turn the dough out onto a lightly floured surface and knead for 8-10 minutes by hand. Dough will be sticky at first, and get less sticky as you knead, so I add extra flour a tablespoon at a time if needed. The dough should still be slightly sticky to the touch but feel smooth and elastic (I find 4 ½ cups is perfect for me every time!).
Let the dough rise. Lightly grease a large bowl, and place dough into the bowl, turning once to coat. Cover the bowl and allow to rise until doubled in size, about 1 hour (for instant or rapid-rise yeast), or 2 hours (if using active dry yeast).
Make the topping. While the dough rises, make the topping. In a medium saucepan, over medium heat combine the butter, brown sugar, maple syrup, and salt. Bring to a boil and let it simmer for a few minutes. Remove from the heat and stir in the vanilla. Set aside.
Roll out the dough. Turn the dough out onto a lightly floured surface, and roll out the dough into a 18x12 inches rectangle.
Spread filling. In a small bowl, stir together the brown sugar and cinnamon. Spread the dough with the softened butter , leaving about a ½-inch border at the top long edge. Sprinkle the brown sugar cinnamon mixture over the butter, pressing down lightly.
Cut rolls. Starting on the long edge with filling, roll up the dough tightly into a log. Pinch the dough to seal. Using a serrated knife cut the log into 12 equal rolls. You can also cut the rolls using a piece of thread or unflavored dental floss,which I find gives the cleanest cuts. I place a long piece of thread underneath the dough, bring up the thread on each side, criss cross it, and then pull the thread through the dough so it cuts right through leaving the spiral intact.
Let rolls rise. Grease a 9”x13” baking dish with butter or non-stick cooking spray. Pour the topping evenly into the bottom of the pan. Sprinkle the chopped pecans over the topping. Place rolls into pan spiral side up. Cover the baking dish and let rise in a warm, draft free place for 45 minutes until the rolls are slightly puffy, and nearly doubled in size. If you used active dry yeast, the second rise time will be near 75 minutes.
Bake rolls. Near the end of the second rise time, position a rack in the center of your oven and preheat the oven to 350°F/177°C. Bake rolls in the preheated oven for 30-35 minutes until golden brown. Let cool in the pan for about 20 minutes, then invert the buns out, one by one onto a serving platter, spooning over any topping that’s still in the pan on top of the buns.