Combine the pumpkin puree, lukewarm milk, egg, sugar and instant yeast in the bowl of a stand mixer. The milk should be warm, not hot, 95°F to 105°F.

Add the flour, salt and pumpkin pie spice if using. Mix with the dough hook on low until no dry flour remains and a rough dough forms, 2 to 3 minutes.

Add the softened butter one small piece at a time, letting each absorb before adding the next. Knead on low-medium for 8 to 10 minutes total, until smooth, elastic, cohesive around the hook and slightly tacky. The dough need not clear the bowl. Add flour only if genuinely wet, in 5 g increments, ideally under 20 g total.

Shape into a ball, place in a lightly greased bowl, cover, and rise in a warm, draft-free spot until roughly doubled, 60 to 90 minutes.

Deflate gently and divide into 12 portions of about 74 g. Shape each into a tight ball, seam underneath. Rest 5 to 10 minutes, loosely covered.

Flatten each ball between your palms into a thick disk about 1 inch high. Lightly oil the tips of clean kitchen scissors and make 8 evenly spaced cuts from the outer edge inward, deep enough that the lobes separate down the sides, stopping before the center so the sections stay connected. Nudge the sections gently outward so the disk opens into one of those rolls that look like pumpkins rather than a scored bun. Place on a parchment-lined baking sheet with space between them. If the dough spreads while cutting, chill the disks 10 to 15 minutes.

Cover loosely and rise 30 to 45 minutes, until puffy but not doubled and a fingertip press springs back slowly. The grooves must still be clearly visible.

Heat the oven to 350°F. Whisk the finishing egg with 1 teaspoon milk and brush the rolls lightly. Press one pepita flat into the center of each without pushing it deep.

Brush with melted butter immediately out of the oven. Cool at least 10 minutes before serving.