Cheesy Challah Bread

1. Combine first 3 ingredients in a large bowl; let stand until bubbly. Stir in butter, salt, 5 egg yolks, and 3 eggs. Stir in gruyere and chives. Lightly spoon flours into dry measuring cups; level with a knife. Add bread flour about 2 1/4 cups and about 2 3/4 cups all-purpose flour to yeast mixture, stirring until a soft dough forms (dough will be sticky).
2. Turn dough out onto a lightly floured surface. Knead until smooth and elastic. Place dough in a large bowl coated with cooking spray, turning to coat top. Cover with plastic wrap, and let rise in a warm place, free from drafts, for 45 minutes or until doubled in size. Punch down dough; cover and let rise 35 minutes or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.)
3. Divide dough into 6 equal portions. Roll each portion into a ball. Roll each ball into a rope about 15 inches long. Place 3 ropes parallel to one another; braid ropes. Pinch ends together, and tuck under loaf. Repeat procedure with remaining 3 ropes. Place loaves on a baking sheet lined with parchment paper; coat with cooking spray. Cover and let rise 30 minutes or until doubled in size.
4. Preheat oven to 375u0b0F.
5. Combine 1 egg and 2 tablespoons water, stirring well with a whisk. Brush loaves gently with egg mixture. Sprinkle loaves evenly with Parmigiano-Reggiano. Bake at 375u0b0 for 25 minutes or until golden. Remove from baking sheet; cool on a wire rack.