Step 1

Heat the milk and butter in a medium saucepan over medium-low heat until the butter melts, about 5 minutes. Remove from heat; let cool for about 5 minutes. Add the sweet potato and egg and stir to combine (some lumps are ok).

Step 2

Place 3 cups of the flour, sugar, yeast, orange zest, cardamom, and salt in the bowl of a stand mixer fitted with the dough hook. Add the warm milk mixture. Knead the dough on low speed until smooth and elastic, about 8 minutes. If the dough is too sticky to handle, knead in up to 1/4 cup more flour a tablespoon at a time.

Step 3

Remove the dough from the bowl. Lightly grease the bowl with butter, then return the dough to the bowl. Cover with plastic wrap and let rise in a warm, draft-free spot until the dough has doubled in size, 1 to 1 1/2 hours.

Step 4

Place the brown sugar, butter, orange zest, salt, and cardamom in a small bowl and mix until combined and spreadable.

Step 5

Coat a 9x13-inch baking dish with butter. Place the dough on a very lightly floured work surface. Roll it into a 10x12-inch rectangle with the longer side facing you. Spread the cardamom butter evenly over the dough. Sprinkle with the pistachios and gently press them into the butter. Tightly roll up the dough and pinch the top seam closed.

Step 6

Cut the roll crosswise into 12 pieces. Place the buns in the baking dish cut-side up. Cover loosely with plastic wrap and let rise in a warm place until the buns have puffed and are nestled closer to each other, 1 hour to 90 minutes.

Step 7

Arrange a rack in the middle of the oven and heat to 350°F. Uncover the buns and brush with the beaten egg. Bake until golden-brown and puffed, 25 to 30 minutes. Let cool for 10 minutes.

Step 8

Place the powdered sugar, orange juice, and salt in a small bowl and stir with a fork until a thick but pourable glaze forms. Drizzle over the still-warm rolls.