Warm the whole milk to approximately 105–115°F (40–46°C). Stir it with the yeast and a small amount of the granulated sugar, then let the mixture stand for 5–10 minutes until foamy.

Add the remaining sugar, butter, eggs, flour, and salt. Mix until a soft dough forms, adding only a little extra flour if necessary.

Knead the dough for about 5 minutes by hand or with a dough hook until smooth and elastic. It should feel soft and slightly tacky rather than stiff.

Place the dough in a lightly greased bowl, cover, and let it rise in a warm, draft-free place for about 1 hour, or until doubled in size.

Roll the dough into an approximately 16-by-24-inch rectangle. Spread it with softened butter, then sprinkle the brown sugar and cinnamon evenly over the surface.

Roll the dough tightly from the long side into a log. Cut it into 12 equal pieces and arrange them in a greased 9-by-13-inch baking pan.

Cover the pan and let the rolls rise for 25–40 minutes, until noticeably puffy. Bake at 350°F (175°C) for 20–25 minutes, until lightly golden and cooked through in the center.

Beat the cream cheese, butter, powdered sugar, and vanilla until smooth. Spread the frosting over the warm, not piping-hot, cinnamon rolls before serving.