In a light-colored saucepan, melt unsalted butter over medium heat, stirring constantly until golden and nutty, about 5-7 minutes.

In a bowl, combine active dry or instant yeast, granulated sugar, and lukewarm milk. Stir gently and allow to sit for about 5-10 minutes until foamy.

Add cooled brown butter, flour, beaten egg, pumpkin puree, salt, dried rosemary, and ground cardamom to the yeast mixture. Mix until a shaggy dough forms.

Knead dough on medium-low speed for about 20-25 minutes until smooth and elastic.

Transfer the dough to a lightly oiled bowl, cover, and let it rise in a warm area until doubled in size, about 45-60 minutes.

Gently punch down the dough, divide into 8 pieces, and shape each into a ball. Place in a greased baking tin, cover, and let rise for another 45-60 minutes.

Preheat your oven to 375°F (190°C).

Whisk together the remaining beaten egg with 1 tablespoon of milk. Brush over the tops of the rolls.

Bake for about 20-25 minutes until golden brown and hollow when tapped.

Allow to cool in the tin for 5 minutes before transferring to a wire rack.