In a large bowl, whisk together 4 cups flour, 1½ teaspoon instant yeast, 2 tablespoon sugar, and 1½ teaspoon salt until well combined.

Warm ¾ cup milk and 3 tablespoon butter in the microwave for 45-60 seconds until butter melts and mixture is lukewarm (not hot). Stir in 1 cup pumpkin puree and 1 egg until smooth.

Pour the pumpkin mixture into the flour mixture and stir with a wooden spoon until a shaggy dough forms, about 1 minute.

Turn dough onto a lightly floured surface and knead for 6-8 minutes until smooth and elastic. The dough will feel slightly sticky but should pull away from your hands cleanly.

Place dough in a lightly oiled bowl, turning once to coat all sides. Cover with a damp towel and let rise in a warm place for 1½ to 2 hours until doubled in size.

Punch down the risen dough and divide into 9 equal pieces (about 3 oz each). Shape each piece into a ball by pulling the edges toward the center, pinching to seal, then rolling gently between your palms until smooth.

Arrange balls in a greased 9x9 inch baking dish, leaving slight space between each. Cover and let rise for 45-60 minutes until puffy and touching each other.

Preheat oven to 375°F. Beat together 1 egg and 1 tablespoon water, then brush over the tops of the rolls for a glossy finish.

Bake for 18-22 minutes until tops are deep golden brown and internal temperature reaches 190°F. Cool in pan for 5 minutes before serving.