Place milk, 4 tablespoons melted butter, water, beaten egg, bread flour, pudding mix, sugar, salt, and yeast in the order recommended by the manufacturer. Select Dough cycle.

Remove dough from machine after the cycle is done; knead 3 to 5 minutes. Roll out to a large rectangle. Grease a 9x13-inch baking pan.

Combine brown sugar, 1/2 cup softened butter, and cinnamon in a bowl; spread over dough. Sprinkle walnuts and raisins over top.

Roll dough into a log, starting with the widest end; pinch to seal seams. Cut into 1/2- to 1-inch slices; place in the prepared baking pan. Place in a draft-free space; let rise until doubled in volume.

Preheat the oven to 350 degrees F (175 degrees C).

Bake in the preheated oven for 15 to 20 minutes.

Meanwhile, combine confectioners’ sugar, 4 tablespoons softened butter, milk, and vanilla in a small bowl; spread over warm cinnamon rolls.