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Step 1
Heat the oven to 425°F with a rack in the middle position. Mist a rimmed baking sheet with cooking spray. Place the squash halves cut side down on the prepared baking sheet and roast until a skewer inserted through the neck of the squash meets no resistance, 35 to 40 minutes. Remove from the oven, turn the squash halves cut side up and set aside until cool enough to handle.
Step 2
Scoop the flesh out of the skins into a large bowl; discard the skins. Using a silicone spatula, mash the flesh until smooth. If the squash is still warm, let cool completely. Measure 230 grams (1 cup) of the squash into a medium bowl; reserve the remainder for another use. To the squash, add the milk, honey and 2 eggs. Whisk until homogeneous; set aside. Mist a large bowl with cooking spray.
Step 3
In a stand mixer with the dough hook, mix the flour, yeast, allspice and salt on low until combined, about 20 seconds. With the mixer running, gradually pour in the squash mixture, then continue mixing until a wet, slightly lumpy dough forms, about 2 minutes, scraping the bowl once. Increase to medium and knead the mixture, scraping the bowl once or twice, until it pulls away cleanly from the sides, 5 to 6 minutes. If it sticks to the bowl, add 2 tablespoons flour and knead for about 2 minutes before assessing if even more flour is needed.
Step 4
Add the butter one piece at a time and mix until it is almost fully incorporated, about 30 seconds, before adding another piece. After all the butter has been added, mix on medium until the dough is smooth and elastic and pulls away from the sides of the bowl, 7 to 9 minutes. Detach the bowl and hook from the mixer, then lift out the hook with dough clinging to it; the dough should fall from the hook and stretch into a translucent “pane.” If it breaks before forming a pane, continue kneading on medium for another 1 to 2 minutes, then test again. The dough will resemble a stretchy, webby batter.
Step 5
Using a plastic dough scraper or silicone spatula, scrape the dough into the prepared bowl, cover tightly with plastic wrap and let rise at room temperature until bubbles form on the surface, about 1 hour. Refrigerate for at least 4 hours or up to 24 hours.
Step 6
Line a rimmed baking sheet with kitchen parchment. Lightly flour the counter. Turn the dough out onto the counter and divide it into 3 even portions. Lightly flour your hands and roll each portion into an 18-inch rope.
Step 7
Position the ropes perpendicular to the counter’s edge but parallel to each other; flour the counter as needed. Firmly pinch together the far ends of the ropes.
Step 8
Flour your fingers, then lift the right rope, cross it over the middle rope and lay it between the other 2; adjust the spacing of the ropes as you go.
Step 9
Now cross the left rope over the new middle rope and lay it between the other 2.
Step 10
Repeat the braiding until you reach the ends of the ropes. Firmly pinch together the ends. Tuck the 2 pinched ends under the loaf.
Step 11
Transfer the loaf to the prepared baking sheet; gently reshape, if needed. Mist a large sheet of plastic wrap with cooking spray and drape it, greased side down, over the loaf. Lay a kitchen towel on top. Let rise at room temperature until doubled in size and the dough springs back slowly when lightly pressed with a fingertip, about 1½ hours. Meanwhile, heat the oven to 350°F with a rack in the middle position.
Step 12
In a small bowl, beat the remaining egg. Lightly brush the dough with the beaten egg, then sprinkle evenly with the pumpkin seeds. Bake until golden brown and the center of the loaf reaches 190°F to 200°F, 30 to 35 minutes. Let the loaf cool on the baking sheet on a wire rack for about 10 minutes. Transfer the bread, still on the parchment, directly to the rack. Cool for at least 1 hour before slicing.