Combine the flour, sugar, salt, and yeast in a large mixing bowl. In a separate bowl, whisk together the warm milk, eggs, softened butter, and vanilla extract. Gradually add the wet ingredients to the dry ingredients, mixing until a soft dough forms.
Knead the dough on a lightly floured surface for 8-10 minutes until smooth and elastic. Form into a ball and place in a greased bowl, covering with plastic wrap or a damp cloth.
Allow to rise in a warm place for about 1 hour, or until doubled in size. For optimal rising, place your dough in an oven with just the light turned on.
While the dough rises, steam the kabocha squash until fork-tender (approximately 15 minutes). Remove the skin and mash until smooth.
Mix in the brown sugar, honey, cinnamon, nutmeg, ginger, and melted butter. Allow the mixture to cool completely.
After the first rise, punch down the dough and divide it into 8 equal portions. Take each portion and flatten it into a disc about 4 inches in diameter.
Place a heaping tablespoon of the pumpkin filling in the center, then bring the edges up and pinch to seal completely. Place seam-side down on a parchment-lined baking sheet.
Arrange the dough balls in a circular pattern to create the pumpkin shape, leaving a small space in the center for the "stem" later.
Cover the shaped dough with a damp cloth and let rise for another 30 minutes. Preheat your oven to 350°F (175°C).
Once risen, use kitchen scissors to make shallow cuts from top to bottom around each dough ball to create the pumpkin's signature ridges. Brush with beaten egg for a golden finish.
Place the cinnamon stick in the center as a stem and sprinkle pumpkin seeds around the base if desired.
Bake for 25-30 minutes, or until the bread is golden brown and sounds hollow when tapped on the bottom. If the top browns too quickly, cover loosely with aluminum foil.
The internal temperature should reach 190°F (88°C) when fully baked. Allow to cool slightly before serving.