Place milk, water, melted butter, egg, bread flour, pudding mix, sugar, salt, and yeast into a bread machine in the order listed. Run Dough cycle. Remove dough from the machine after the cycle is done, about 90 minutes.

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 softened butter over the rectangle, then sprinkle brown sugar mixture over top.

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 oven to 350 degrees F (175 degrees C).

Bake rolls in the oven until golden brown, 15 to 20 minutes. Remove from the oven and let cool for 10 minutes.