Pull Apart Pumpkin Brioche

Name: Pull-Apart Pumpkin Brioche
Ingredients: 10 tablespoons unsalted butter, at room temperature; 2.75 cups all-purpose flour, divided; 0.5 cup shredded Cheddar cheese; 3 large eggs; 0.25 cup water; 0.25 cup nonfat dry milk; 3 tablespoons pumpkin puree; 3 tablespoons white sugar; 1 tablespoon instant yeast; 1.25 teaspoons salt; kitchen string; 1 egg white; 1 tablespoon milk; 1 cinnamon stick