In a stand mixer bowl, combine 1 cup flour, yeast, sugar and salt. Heat milk, water and butter to 120-130°F; butter does not need to melt. Add warm milk mixture to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Add egg; beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Prepare topping: Heat butter, brown sugar and corn syrup; stir until butter is melted and ingredients are well blended. Pour into greased 13x9-inch cake pan. Sprinkle pecans evenly over topping.
Prepare filling: In a small bowl, combine brown sugar, granulated sugar and cinnamon; mix to combine.
Turn dough onto lightly floured surface; punch down. Roll or pat to a 15x12-inch rectangle. Spread with softened butter. Sprinkle cinnamon-sugar mixture over dough. Starting with shorter side, roll up tightly. Pinch edges to seal. Cut into 12 slices. Place buns, cut side up, on Topping in pan. Cover; let rise in warm place until indentation remains when lightly touched.
Preheat oven to 350°F.
Bake for 25 to 35 minutes, or until golden brown. Remove from oven; cover pan with foil. Invert pan onto rack. Let sit 1 minute; remove pan. Cool. Be careful as caramelized topping is dangerously hot.