Warm the milk in a microwave-safe bowl for 45 seconds to 1 minute until it registers 115°F.

In a stand mixer bowl fitted with a paddle attachment, sprinkle the yeast over the warm milk. Add the sugar and let sit until foamy, about 5 minutes. Then add 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 more flour if 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 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.

Roll the dough tightly from the short side without the margin. 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 dental floss or a serrated knife.

Line a 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.