Prepare the Brown Butter: Melt 2 tablespoons of unsalted butter over medium heat until golden and nutty. Cool before proceeding.

Activate the Yeast: Combine 2 1/4 teaspoons of yeast, 1 1/2 tablespoons of sugar, and 1/4 cup of lukewarm milk. Let it sit until foamy.

Mix the Dough: Add cooled brown butter, 2 cups flour, 1 egg, 1/2 cup pumpkin puree, 3/4 teaspoon salt, 1 1/2 teaspoons dried rosemary, and 3/4 teaspoon ground cardamom to the mixer. Mix on low, then knead on medium until smooth.

First Proofing: Cover the mixture and let it rise for 45 minutes to 1 hour until doubled in size.

Shape the Rolls: Divide the dough into 8 pieces, shape into rolls, place in a greased tin, cover, and let proof again for 45 minutes to 1 hour.

Apply the Egg Wash: Whisk together 1 egg and 1 tablespoon milk or water, then brush over the rolls.

Bake the Rolls: Bake in a preheated oven at 375°F for 20-25 minutes until golden brown.

Cool and Serve: Allow to cool in the pan for 5 minutes, then transfer to a wire rack. Serve warm.