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In a small bowl, stir together the yeast and maple syrup. Sprinkle the yeast over the surface and stir to dissolve. Let sit for 10 minutes until foamy.
Pour the yeast into the bowl of a stand mixer fitted with a dough hook. Add the pumpkin puree, 4 eggs, and the milk. Add the cinnamon and salt. Mix to combine.
Add the flour a cup at a time to combine, then cut the butter into chunks and add them, bit by bit, until the dough has completely absorbed the butter. Continue to mix for 4 to 5 minutes, to make a soft, sticky dough. Cover the bowl with plastic wrap and allow to rise for an hour in a draft-free place, until doubled in size.
Push the dough down gently with your hands, then cover and refrigerate 4 hours, or preferably overnight, to let the flavors develop.
Butter a 9 x 5 loaf pan, a brioche mold, or three 3 x 6 loaf tins. If using a brioche tin, it’s traditional to nestle a rounded ball of dough into the top. If using loaf tins, you may want to divide the dough into two or three large balls. Let the dough rise again until nearly doubled.
Preheat the oven to 400 degrees. Beat the remaining egg and brush the surface of the dough with it. Pierce the dough in a few places with the tip of a knife. Bake for 10 minutes, then reduce the heat to 325 degrees and continue baking for 20 more minutes for a brioche mold or large loaf pan, or 10 minutes more for small loaf pans. Cool for 15 minutes in the pans, then turn the brioche out and cool completely on a rack before slicing.