Pull-Apart Pumpkin Brioche

Combine butter, 2 1/2 cup flour, Cheddar cheese, eggs, water, dry milk, pumpkin, sugar, yeast, and salt in the bowl of a stand mixer. Mix on medium-high speed until a smooth and shiny dough forms, about 15 minutes.

Sprinkle most of the remaining 1/4 cup flour onto a work surface and turn dough out on top. Form into a ball. Place in a greased bowl, cover with plastic wrap, and let rest until doubled in volume, about 1 hour.

Transfer dough to the refrigerator and chill for 3 hours.

Lay out 2 pieces of long kitchen string or twine onto lightly floured parchment paper to form an X. Lay another pair of strings across the X and repeat until the circle is complete. Place the dough ball on the center point and tie each string over the top of the dough. Trim ends. Cover dough with plastic wrap and let rise in a warm place until puffy and doubled in volume, 2 to 3 hours.

Preheat the oven to 400 degrees F (200 degrees C). Beat egg white and milk together for the glaze. Unwrap dough and brush with glaze. Lift the parchment paper onto a baking sheet.

Bake in the preheated oven for 10 minutes. Reduce oven temperature to 350 degrees F (175 degrees C). Continue baking, tenting with aluminum foil after 15 minutes, for 30 to 35 minutes. Let bread cool on a wire rack until no longer hot to the touch.

Flip bread over; cut the kitchen strings on the bottom and carefully pull them out. Poke cinnamon stick through the center of the top of the bread.