Stir the warm milk, yeast, and sugar in a large bowl and let sit 5 minutes until foamy.

Mix in the melted butter and egg, then add the flour and salt. Stir until a shaggy dough forms, then knead on a floured surface for 6 to 8 minutes until smooth and springy.

Place the dough in a greased bowl, cover, and let rise in a warm spot until doubled, about 1 to 1.5 hours.

Beat the softened butter and peanut butter together until smooth, then stir in the brown sugar and cinnamon until a thick paste forms. Set aside at room temperature.

Punch down the dough and roll it into a 16x12-inch rectangle about 1/4 inch thick. Spread the filling across the dough, leaving a 1/2 inch border on one long side.

Roll the dough tightly from the opposite long side into a log and pinch the seam. Cut into 12 even slices and arrange cut side up in a buttered 9x13-inch pan. Cover loosely and let rise until puffy, 30 to 45 minutes.

Preheat the oven to 350°F (175°C). Bake the rolls for 20 to 22 minutes until golden and a thermometer reads about 190°F (88°C). Cool in the pan for 10 minutes.

Beat the cream cheese, butter, powdered sugar, vanilla, and 1 tablespoon milk until smooth, adding the second tablespoon of milk only if needed. Spoon the frosting over the warm rolls and serve.