Prepare the dough: In a large bowl, whisk together flour, sugar, yeast, salt, cinnamon, and nutmeg until well combined. In a separate bowl, mix pumpkin puree, plant milk, melted vegan butter, and maple syrup until smooth.
Combine wet and dry ingredients: Pour the wet mixture into the dry ingredients and stir until a shaggy dough forms. Turn onto a floured surface and knead for 8-10 minutes until smooth and elastic. If using a stand mixer, knead with the dough hook for 5-7 minutes.
First rise: Place dough in a lightly oiled bowl, cover with a damp cloth, and let rise in a warm place for 1-1.5 hours until doubled in size. The dough should leave an indentation when poked with your finger.
Make the filling: While dough rises, mix softened vegan butter with pumpkin puree until smooth. Add brown sugar, cinnamon, and pumpkin pie spice, stirring until completely incorporated.
Roll out the dough: On a floured surface, roll the risen dough into a large rectangle approximately 18×14 inches. The dough should be about ¼ inch thick and have even thickness throughout.
Add the filling: Spread the pumpkin-cinnamon mixture evenly over the dough, leaving a ½-inch border around the edges. Sprinkle with chopped pecans if using.
Roll and slice: Starting from the long edge, tightly roll the dough into a log. Using a sharp knife or unflavored dental floss, cut into 12 equal rolls, each about 1.5 inches thick.
Second rise: Place rolls in a greased 9×13 baking dish, leaving a little space between each. Cover and let rise for 30-45 minutes until puffy and touching one another.
Preheat and bake: About 20 minutes before the second rise is complete, preheat oven to 350°F (175°C). Bake rolls for 25-30 minutes until golden brown and cooked through.
Prepare frosting: While rolls bake, beat vegan cream cheese and butter until fluffy. Add powdered sugar gradually, then mix in maple syrup, vanilla, and salt until smooth and creamy.
Frost and serve: Allow rolls to cool for 5-10 minutes before spreading generously with frosting. The warmth will create that signature gooey texture as the frosting slightly melts into the rolls.