In a small microwave-safe bowl, warm the milk by microwaving it for 45 seconds to 1 minute, until it registers 115°F on a thermometer and feels like warm bath water.

Place the warmed milk in the bowl of a stand mixer fitted with the paddle attachment and sprinkle the yeast on top. If using active dry yeast, add the sugar now and let the yeast sit with the sugar until foamy, about 5 minutes.

Add the melted butter, egg, and egg yolk. Mix on medium speed until well combined, 30 seconds.

Remove the bowl from the mixer and use a wooden spoon to stir in the flour and salt until a dough begins to form.

Place the dough hook on the stand mixer and return the bowl to the mixer. Mix the dough on medium speed until it comes together and feels soft and slightly sticky, 8 to 10 minutes.

If it’s too sticky, add another 1 to 3 tablespoons bread flour, 1 tablespoon at a time.

Transfer the dough ball to a greased bowl, cover with plastic wrap, and let rise until doubled in size, 1 to 1½ hours.

Generously dust a surface with flour. Turn out the dough and roll it into an 10 × 14-inch rectangle.

Spread the softened butter over the dough, leaving a ¼-inch margin at the far short side of the rectangle.

Mix the brown sugar and cinnamon and sprinkle over the butter, then rub the mixture into the butter.

Tightly roll up the dough from the short side without the margin and seal the far edge of the dough.

Cut the dough into nine 1-inch slices and place in a prepared pan. Cover and let rise again, 45 minutes to 1 hour.

Preheat the oven to 350°F.

Once risen, bake until golden brown on the edges, 20 to 25 minutes.

Cool for 10 minutes.

In a stand mixer fitted with the whisk attachment, combine the cream cheese, powdered sugar, butter, and vanilla.

Beat on low speed for 30 seconds, then increase to medium-high speed until smooth and fluffy, 1 to 2 minutes.

Spread the frosting over the warm rolls and serve.