In a large bowl, stir together 5 cups of flour, 1/2 cup sugar, salt and yeast.
In a 1- to 2- quart pan, combine milk, water, and 1/4 cup butter (cut up).
Place over low heat and cook until warm (120 degrees); butter does not have to melt completely.
Gradually add liquid mixture and eggs to dry ingredients, mixing to blend.

To mix with dough hook: add 1/2 cup flour and beat at high speed until dough pulls cleanly away from sides of bowl and feels only slightly sticky, about 4 minutes; add additional flour, if necessary.

To mix with a spoon: beat in 1/2 cup flour until dough is stretchy; add another 1/4 cup flour if dough is still sticky. Turn dough out onto a floured board and knead until smooth and elastic, 8 to 12 minutes; add more flour if required to prevent sticking.

Place dough in a greased bowl, turning over to grease top. cover with plastic wrap; let rise in a warm place until double, about 45 minutes.
Punch dough down.
Divide in half.
On a floured board, roll each half out into a 9-by 18-inch rectangle.
Melt remaining 1/2 cup butter.
Brush 2 tablespoons butter over each piece of dough.
Set aside remaining butter.
Mix together 1/4 cup of granulated sugar, cinnamon, and 1/4 cup brown sugar. sprinkle sugar mixture evenly over dough.

From a long side, roll each portion into a log.
Pinch edges to seal.
Cut each portion crosswise into 12 equal pieces.
Use 4 round cake pans, each 8 inches across, or 3 round cake pans, each 9 inches across.
Brush each pan with about 1 tablespoon of reserved melted butter, then sprinkle each with about 2 tablespoons brown sugar.
Set rolls cut side up in pan, placing 6 in each 8-inch pan or 8 in each 9-inch pan.
Cover lightly with plastic wrap and chill at least 2 hours or up to 24 hours.

Before baking, let rolls stand at room temperature for 20 minutes.
Uncover and bake in a 350° degree oven until golden brown, 25 to 35 minutes.
Immediately invert onto serving tray.