Combine 1 cup flour, sugar, undissolved yeast and salt in a large mixing bowl. Heat milk, water, onion, and butter until very warm (120° to 130°F). Add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Roll dough to 18 x 12-inch rectangle. Spread Chicken Filling evenly over dough. Roll up tightly as for a jelly roll, beginning at long end. Pinch seam to seal. Place, seam side down, on greased baking sheet. Form into ring; pinch ends together to seal. With sharp knife, cut 16 slits, starting from outer edge, 3 / 4 of the way through dough. Turn each section on its side to show filling. Cover; let rise in warm, draft-free place until doubled in size, about 45 minutes.
Bake at 375°F for 35 to 40 minutes or until done. Remove from sheet; serve warm. Refrigerate leftovers.
Chicken Filling: Combine mayonnaise, blue cheese, shredded pepper Jack cheese, shredded cheddar cheese, diced cooked chicken and chicken wing sauce in medium size bowl. Refrigerate until ready to use.