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, using a pizza cutter, cut strips of the dough about 1½-inch thick. Roll the dough to create a swirl. Pinch the seam closed.
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. If you don't want to invert, serve directly from the pan.