Make the dough: Place milk, water, melted butter, egg, bread flour, pudding mix, sugar, salt, and yeast into a bread machine in the order listed, or follow the order recommended by the manufacturer if different. Run Dough cycle. Remove dough from the machine after the cycle is done, about 90 minutes.
When the dough is almost finished, start the filling: Mix brown sugar, pecans, and cinnamon together in a bowl until well combined. Butter a 9x13-inch baking pan.
Turn dough out onto a lightly floured surface and roll into a 17x10-inch rectangle. Spread 1/2 cup softened butter over the rectangle, then sprinkle brown sugar mixture over top.
Beginning with the long side, roll dough over filling into a log; cut log into sixteen 1-inch slices. Place slices, cut-sides up, into the prepared pan. Let rise in a warm place until doubled in volume, about 45 minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Bake rolls in the preheated oven until golden brown, 15 to 20 minutes. Remove from the oven and let cool for 10 minutes.
While the rolls are cooling, make the frosting: Stir confectioners' sugar, softened butter, cream cheese, milk, and vanilla together in a bowl until well combined. Spread over warm rolls.
