In the bowl of a stand mixer fitted with the dough hook, combine the yeast, warm milk, and sugar. Stir lightly with a whisk or fork and let stand for about 10 minutes, until the mixture becomes foamy.

Add the eggs and mix on medium speed. Gradually add the flour, vanilla extract, and salt, mixing until incorporated. Add the softened butter, cut into small cubes, and continue kneading for about 15 minutes, or until the dough is smooth and elastic.

Cover the bowl with plastic wrap or a clean kitchen towel and let the dough rise in a warm place for about 1½ hours, until doubled in size.

Meanwhile, prepare the cinnamon sugar filling by mixing the brown sugar and cinnamon together in a medium bowl using a spatula or wooden spoon.

Alternatively, prepare the cinnamon spread by beating the butter, brown sugar, white sugar, and cinnamon together in the stand mixer fitted with the paddle attachment (also known as a "guitar hook") until light and fluffy, about 3 to 4 minutes.

Once the dough has risen, transfer it to a lightly floured surface. Using a rolling pin, roll it into a large rectangle about ½ cm thick. Spread the very soft butter (or cinnamon spread) evenly over the dough using an offset spatula. Sprinkle the cinnamon sugar mixture evenly across the surface and gently press it into the dough with your hands.

Roll up the dough tightly into a log, then cut into rolls about 2 inches/5 cm wide using a sharp knife or unflavored dental floss for clean cuts. Arrange the rolls on a baking sheet lined with parchment paper, spacing them apart to allow room for rising. Cover loosely with a towel and let rise again for about 45 minutes, until doubled in size.

Bake the cinnamon rolls for about 25 minutes, or until deeply golden on top and cooked through.

While the rolls bake, prepare the frosting by mixing the butter, cream cheese, and powdered sugar together in a medium bowl using a hand mixer or a whisk until smooth and creamy.

Remove the rolls from the oven and immediately spread the frosting generously over the warm rolls using a spoon or an offset spatula. Serve warm.