Mix the dough: In a large mixing bowl or stand mixer bowl, stir together the warm milk, yeast, sugar, pumpkin puree, egg, cooled melted butter, vanilla, and pumpkin pie spice. Add the salt and 4¼ cups (510 g) flour. Mix until a soft dough forms.
Knead: Knead with a dough hook on low to medium-low speed for 8 to 10 minutes, or by hand for 10 to 12 minutes, until smooth and elastic. If the dough remains very wet, add flour 1 tablespoon at a time, up to the remaining ¼ cup (30 g). The finished dough should be soft and slightly tacky.
First rise: Place in a lightly greased bowl, cover, and let rise in a warm spot for 1½ to 2 hours, or until roughly doubled.
Prepare the topping: Grease a 9-by-13-inch metal baking pan with sides at least 2 inches tall. Melt the topping butter in a small saucepan over medium-low heat. Stir in the brown sugar, maple syrup, cream, and salt. Bring to a gentle simmer, stirring, and simmer for about 1 minute once smooth and bubbling. Remove from heat and stir in the vanilla. Pour into the pan, scatter with pecans, and cool until lukewarm.
Fill: Mix the filling brown sugar, cinnamon, pumpkin pie spice, and salt. Roll the risen dough into an 18-by-12-inch rectangle on a lightly floured surface. Spread with the softened filling butter, leaving a ½-inch bare strip along one long edge. Sprinkle with the sugar mixture and gently press it into the butter.
Shape: Starting from the opposite long edge, roll into an 18-inch log. Pinch the seam closed. Cut into 12 equal pieces and arrange cut-side up over the topping in three rows of four.
Second rise: Cover and let rise for 45 to 75 minutes, or until puffy and filling much of the space between the buns. For overnight preparation, refrigerate immediately after shaping instead; see Notes.
Bake: Heat the oven to 350°F. Place the pan on a rimmed baking sheet and bake for 30 to 38 minutes. Tent loosely with foil if browning quickly. The bread portion of a center bun should reach about 190°F to 195°F and show no wet, raw dough.
Invert and serve: Cool in the pan for about 5 minutes. Carefully loosen the edges and invert onto a larger heat-safe rimmed serving tray using oven mitts. Lift off the pan and spoon any remaining topping over the buns. Cool for another 10 to 15 minutes before serving.