Start by melting 2 tablespoons of unsalted butter in a light-colored saucepan over medium heat. Stir continuously until it turns golden brown and emits a nutty aroma, about 5–7 minutes. Pour the butter into a heat-proof container and set it aside to cool.

In the stand mixer bowl, combine 2 1/4 teaspoons of active dry yeast, 1 1/2 tablespoons of granulated sugar, and 1/4 cup of lukewarm milk. Let it sit for about 5–10 minutes until frothy.

Add the cooled brown butter, 2 cups of all-purpose flour, 1 egg, 1/2 cup of pumpkin puree, 3/4 teaspoon of salt, 1 1/2 teaspoons of dried rosemary, and 3/4 teaspoon of ground cardamom to the yeast mixture. Knead for 20–25 minutes until the dough pulls away from the bowl.

Transfer the dough to a lightly greased bowl and cover it with a kitchen towel. Allow it to rise in a warm place for about 45–60 minutes until it doubles in size.

Lightly flour your workspace and transfer the risen dough onto it. Divide into 8 equal pieces and shape into smooth balls. Place them in a greased baking tin.

Cover the tin with a towel and let the rolls proof for another 45–60 minutes until they spring back when gently pressed. Preheat your oven to 375°F.

In a small bowl, beat together 1 egg with 1 tablespoon of milk or water. Gently brush this over the tops of the rolls.

Bake for 20–25 minutes, or until golden brown and sound hollow when tapped. Allow to cool slightly in the tin before serving warm.