Warm the milk in a small saucepan or microwave until it reaches 105–110°F.

Whisk the yeast and granulated sugar into the warm milk and let stand for 5–10 minutes, until foamy.

Whisk the egg, melted butter, and salt into the yeast mixture.

Stir in the flour, 1 cup at a time, until a shaggy dough forms.

Knead the dough on a clean work surface for 8–10 minutes, until smooth and elastic.

Spray a large bowl with cooking spray, place the dough in it, and cover. Let rise in a warm place for 1–1 1/2 hours, until doubled in size.

Roll the dough into a 12x18-inch rectangle on a clean work surface.

Spread the softened butter evenly over the dough.

Stir the brown sugar and cinnamon together, then sprinkle the mixture evenly over the butter.

Cut the rectangle into 12 strips, each 1 1/2 inches wide and 12 inches long. Roll the short ends of each strip toward the center, pinch the meeting point into a heart’s bottom point, and press a slight notch between the rounded lobes.

Spray a 9x13-inch baking dish with cooking spray and arrange the rolls in it, pointed ends facing down.

Cover loosely and let rise for 30–45 minutes, until puffy.

Heat the oven to 350°F toward the end of the rise.

Bake for 22–27 minutes, until the rolls are puffed and golden brown.

Beat the cream cheese and softened butter until smooth, then beat in the powdered sugar, vanilla, and milk until creamy.

Let the rolls cool in the dish for 10 minutes, then spread the icing over them.