Combine 3 cups flour, undissolved yeast, sugar and salt in large mixer bowl. Heat milk, water and butter until very warm (120° to 130°F) and add to flour mixture along with the eggs. Beat for 3 minutes until smooth. Stir in enough remaining flour to make soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover and let rest for 10 minutes.
Combine cheese, onions, chives, and garlic powder in a bowl.
Divide dough in half and roll one half into a 15 x 12-inch rectangle. Spread with half the mayonnaise and sprinkle with half of the cheese mixture. Roll up jellyroll style and pinch seams to seal. Slice into 12 slices and place in well greased 13 x 9-inch pan. Repeat with other half of dough. Cover and let rise about 30 to 40 minutes until doubled.
Bake in preheated 375°F for 20 to 25 minutes. Cool in pan about 10 minutes and then remove to wire rack. Store in closed container.