Whisk bread flour, granulated sugar, instant yeast, pumpkin pie spice, cinnamon, and salt in a stand mixer with dough hook until evenly combined. Scrape the bowl to remove any dry pockets.

Add pumpkin puree, eggs, and warm milk, then mix on medium until a smooth dough forms, about 5 minutes. Stop once the dough looks silky and cohesive.

Add softened unsalted butter 1 tablespoon at a time, waiting until each piece is incorporated before adding the next; this takes 10-15 minutes. The dough should stay very soft and start looking glossy as it comes together.

Cover the dough and let it rise at room temperature for 1.5 hours, until doubled in size. Look for a puffy dough that springs back slowly when lightly pressed.

Either refrigerate the dough overnight or shape immediately into a loaf by placing it in a greased 9x5 pan. If shaping right away, proceed to the next rise without delay.

Let the shaped loaf rise for 1.5 hours until it fills the pan and looks visibly expanded. The dough should appear aerated and reach near the top edge of the pan.

Brush the top with egg wash (egg mixed with 1 tablespoon milk). Use a light, even coat so the crust bakes to a deep golden sheen.

Bake at 375°F for 30-35 minutes until deeply golden. The loaf should sound hollow when tapped and look set through the center.

Cool the loaf completely before slicing for clean pieces. Wait until the interior is no longer warm to the touch.