Whisk together the flour, sugar, yeast, and salt. Combine warm milk, melted butter, and egg, then stir into the dry mix. Knead for 8–10 minutes until smooth and elastic.

Place dough in a greased bowl, cover, and let rise in a warm spot until doubled, about 1 hour.

Punch down dough and roll into a 12x18-inch rectangle. Spread with the 4 tbsp soft butter, leaving a ¼-inch border on the far long edge. Mix brown sugar and cinnamon, sprinkle evenly, then top with chocolate chips.

Roll the dough into a tight log, seal the seam, and cut into 12 pieces. Arrange in a greased 9x13-inch pan, cover, and let rise until puffy, 30–45 minutes.

Preheat oven to 350°F (175°C). Bake rolls for 22–25 minutes until golden and cooked through.

While rolls bake, beat cream cheese, 2 tbsp butter, powdered sugar, vanilla, and 1 tbsp milk until smooth, adding more milk as needed. Let rolls cool 5 minutes, then spread frosting over the warm rolls.