Filling
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. Add yeast and sugar and let stand until foamy.
Add the melted butter, egg, and egg yolk. Mix on medium speed until well combined, 30 seconds. Stir in the flour and salt until a dough begins to form.
With a dough hook, knead the dough on medium speed until it comes together and feels soft and slightly sticky, 8 to 10 minutes. If it’s too sticky—meaning it’s sticking to the bottom of the mixer—add another 1 to 3 tablespoons bread flour, 1 tablespoon at a time.
Lightly grease a large bowl with olive oil. Transfer the dough ball to the bowl, then cover with plastic wrap and the warm towel. Allow the dough to rise until doubled in size, 1 to 1½ hours. You will know the dough has risen enough when you poke your finger into the dough about an inch without the indentation bouncing back immediately.
Generously dust a surface with flour. Turn out the dough and use a rolling pin to roll the dough into an 10 × 14-inch rectangle.
Prepare the filling: Spread the softened butter over the dough, leaving a ¼-inch margin at the far short side of the rectangle. In a small bowl, mix together the brown sugar and cinnamon. Use your hands to sprinkle the mixture over the butter, then gently rub the brown sugar mixture into the butter.
Starting from the short side without the margin, very tightly roll up the dough. Seal the far edge of the dough as best you can by pinching the dough together just slightly, then make sure the dough log is seam-side down. Cut a ½ inch off the ends of the dough, as the ends won’t have enough filling; feel free to discard (or bake separately as yummy extras). Use your hands to give the dough log a gentle push inwards on both ends so that it compacts slightly, as it may have stretched out a bit during the rolling process.
Using unflavored dental floss or a serrated knife, cut the dough into nine 1-inch slices.
Line a round or square 9-inch pan with parchment paper. Place the rolls in the prepared baking pan. Cover with plastic wrap and a towel and let rise again until the rolls have puffed up, are doubled in size, and touching each other in the pan, 45 minutes to 1 hour.
Meanwhile, preheat the oven to 350°F.
Bake the cinnamon rolls: Once the rolls have risen, remove the plastic wrap and towel and bake until golden brown on the edges, 20 to 25 minutes. Not overbaking the rolls ensures that they will stay soft in the middle. Cool for 10 minutes.
Prepare the cream cheese frosting: In the bowl of 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. (Alternatively, whisk the frosting by hand.) Spread the frosting over the warm rolls and serve.
To store: Cover the whole pan with plastic wrap and foil or place individual cinnamon rolls in airtight containers or silicone bags and store in the fridge for up to 5 days. Reheat the cinnamon rolls individually in the microwave in 15 second intervals until warm.
