In the bowl of a stand mixer, whisk together warm milk, yeast, and 1 tablespoon of the granulated sugar. Let stand for 5 to 7 minutes until frothy.

Add remaining granulated sugar, pumpkin puree, melted butter, eggs, and vanilla. Whisk to combine.

Fit mixer with dough hook. Add flour, pumpkin pie spice, and salt. Knead on low speed for 8 to 10 minutes until smooth, supple, and slightly tacky but not sticky.

Transfer dough to a greased bowl, cover with plastic wrap, and let rise in a warm spot for 60 to 90 minutes until doubled in size.

Punch down risen dough and turn out onto a lightly floured surface. Roll into an even 12x18-inch rectangle.

Spread the softened butter evenly across the dough, leaving a 1/2-inch border at the top edge. In a small bowl, mix brown sugar, cinnamon, and nutmeg, then sprinkle generously over the butter. Scatter chopped toasted pecans evenly across the top.

Starting from the long edge, roll the dough tightly into a snug 18-inch cylinder. Using unflavored dental floss or a sharp serrated knife, slice into 12 equal rolls.

Arrange rolls in a greased 9x13-inch metal baking pan lined with parchment paper. Cover and let rise for 30 to 45 minutes until puffy and touching (or refrigerate overnight for morning bake).

Preheat oven to 350°F (175°C). Optional bakery secret: warm 1/3 cup heavy cream and drizzle between the rolls right before baking.

Bake for 22 to 26 minutes until golden brown and a toothpick inserted into center comes out clean. Cool for 10 minutes on a wire rack.

While warm, beat cream cheese, butter, maple syrup, powdered sugar, vanilla, and heavy cream until silky smooth. Spread generously over warm rolls, garnish with whole toasted pecans, and serve gooey and warm.