Microwave the milk in 20-second intervals until it is warm but not too hot--about 110 degrees Fahrenheit. Add the milk, yeast, and brown sugar to the mixing bowl of a stand mixer. Cover with a towel and let sit for 5 minutes. The milk will be bubbly when it's ready.
Next, add the eggs, vanilla extract, cinnamon, salt, butter, and flour to the mixer. Knead the dough with the hook attachment of your mixer for 7 minutes. If not using a stand mixer, combine the dough with a wooden spoon. Use your hands to knead the dough on a floured surface for 7 minutes.
The dough will be ready when you can press your finger onto it and no dough sticks to your finger when you move it off the dough. If the dough still sticks, knead it for an extra minute or two. Grease the inside of the bowl with olive oil or butter, roll the dough into a ball, and cover with plastic wrap or a towel. Let sit at room temperature for about two hours.