In the bowl of a stand mixer, whisk together 2 tablespoons of the bread flour, yeast, warm milk and sugar. Set aside until foamy, about 10 minutes.
Once foamy, stir in the eggs and pumpkin puree.
Stir 1 cup of the bread flour into the yeast mixture until a thick paste forms.
In the stand mixer fitted with a dough hook, on a low speed, beat in the salt and butter. Mix until combined, 2 to 3 minutes.
Beat in the remaining flour ½ cup at a time, mixing well between each addition, until the dough is soft and pulls away from the sides of the bowl, 3 to 5 minutes.
On a lightly floured surface, knead the dough for an additional minute. Then form it into a large ball. If the dough is too sticky, add more flour as needed.
Grease a large bowl with olive oil and place the dough inside. Roll the dough in the oil to completely coat. Cover the bowl with a clean cloth and let rest at room temperature until doubled in size, 1 to 2 hours.
Preheat the oven to 350F. Line 2 baking sheets with parchment paper and lightly grease the paper.
On a lightly floured surface, divide the dough into 15 portions and shape each portion into a ball. Keep the dough covered with a clean cloth to prevent a skin from forming.
On an unfloured surface, roll one ball of dough into a 16-inch rope.
With the rope, create a loop with a 5-inch tail and a 2-inch tail.
Weave the 5-inch tail around the loop.
Hold the end of the 5-inch tail in place and weave the 2-inch tail into the loop. Tightly pinch the ends together.
Place the roll seam side down 2 inches apart on the baking sheets. Repeat with the remaining dough.
Cover with a clean cloth and let rest for 10 minutes.
Brush the rolls with the egg wash.
Bake until golden brown, 20 to 25 minutes.
Place a toasted pecan in the center of each roll for the stem, then let cool for 5 minutes on the baking sheets.
