First, activate the yeast by mixing it in warm milk with a teaspoon of sugar. Milk has to be between 105 °F and 110 °F to let the yeast bloom, that's about 20 seconds of warming time in the microwave. Let it rest for 10 minutes until the bubbles appear.
Prepare the flour and add a pinch of salt to the bowl, too. In a large mixing dish, assemble the wet ingredients: softened butter, vanilla extract, egg, activated yeast, and lukewarm milk.
Mix it a bit on a low speed, then start adding the flour spoon by spoon.
Keep mixing until the dough forms and reaches a smooth texture. Mixing is the key to fluffy conchas. You can knead it by hand, as well, but it will take a bit more time. The dough will be sticky, but don't add more flour, just keep mixing.
That way you will wake up the gluten and get a smooth but soft dough. This usually lasts 10 or 15 minutes, on low speed, and if your dough is still gooey, dust it with a spoonful of flour.
Place the dough in the greased bowl, cover it with plastic foil, and let it sit for an hour or more.
I like to let it rise twice before shaping my conchas, but if you don't have much time, one time will be enough, as well. If you're using my method, just knead it lightly after it doubles, and wait for one more hour.