Pumpkin Yeast Rolls

Place 1 cup flour, 1½ teaspoons salt, and nutmeg in the bowl of a stand mixer fitted with the paddle attachment; beat at low speed until well combined. Stir together ¼ cup milk and ¼ cup water in a small microwave-safe bowl; heat on high until an instant-read thermometer registers 110° to 115°. Stir in 1 tablespoon maple syrup and yeast. Let stand until foamy, 5 to 10 minutes. Add milk mixture and melted butter to flour mixture; beat at medium speed for 2 minutes. Add pumpkin, 1 egg, and 2 tablespoons maple syrup; beat at medium-high speed for 2 minutes. Gradually add 2¼ cups flour, beating until just combined, stopping to scrape sides of bowl. Switch to the dough hook attachment. Add remaining ¼ cup flour, 1 tablespoon at a time, beating at medium speed until a soft, smooth, elastic dough forms, 6 to 8 minutes. Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°) until doubled in size, 40 minutes to 1 hour. Line a rimmed baking sheet with parchment paper.

Punch down dough. Turn out onto a lightly floured surface; divide dough into 40 equal pieces. Roll each dough piece into a rope about 5 inches long. Place 4 ropes in a hashtag pattern (over, under, over, under). Take one rope end, and cross it over an adjacent piece; repeat with each end. Tuck ends under, pinching together, and place on prepared pan. Repeat with remaining dough ropes. Loosely cover with plastic wrap, and let rise in a warm, draft-free place (75°) until doubled in size, 30 minutes to 1 hour. Preheat oven to 375°. Whisk together remaining 1 egg and remaining 1 tablespoon milk in a small bowl; brush onto dough. Bake until golden brown and an instant-read thermometer inserted in center registers at least 190°, about 15 minutes. Whisk together room temperature butter, remaining 1 tablespoon maple syrup, and remaining ½ teaspoon salt in another small bowl.

Serve with hot rolls.