In a small microwave-safe bowl, warm the milk by microwaving it for 45 seconds to 1 minute until it registers 115°F.

In the bowl of a stand mixer fitted with the paddle attachment, sprinkle the yeast over the warmed milk. Add the sugar if using active dry yeast and let sit until foamy, about 5 minutes. Then add the melted butter, egg, and egg yolk; mix on medium speed until well combined.

Stir in the flour and salt until a dough begins to form.

Knead the dough on medium speed with the dough hook for 8 to 10 minutes until it feels soft and slightly sticky, adding flour as needed.

Lightly grease a large bowl with olive oil, transfer the dough, cover with plastic wrap and a warm towel, and allow to rise until doubled in size, about 1 to 1½ hours.

Dust a surface with flour, turn out the dough, and roll it into a 10 × 14-inch rectangle.

Spread the softened butter over the dough, leaving a ¼-inch margin at one end. Mix brown sugar and cinnamon, sprinkle over the butter, and rub it in gently.

Starting from the short side without the margin, roll the dough tightly. Seal the edge by pinching, cut off ½ inch from both ends, and compact the ends slightly.

Cut the dough into nine 1-inch slices using unflavored dental floss or a serrated knife.

Line a 9-inch round or square baking pan with parchment paper, place rolls in the pan, cover with plastic wrap and a towel, and let rise until puffed and doubled, about 45 minutes to 1 hour.

Preheat the oven to 350°F.

Bake the rolls for 20 to 25 minutes until golden brown on the edges. Cool for 10 minutes.

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

Spread the frosting over warm rolls and serve.