Have each ingredient ready and measured (by weight) before starting, and thoroughly read the notes above. Mix the all-purpose flour, yeast, sugar, and salt in the bowl of a stand mixer at medium speed, just to mix it well.
Add the butter and mix well (using the stand mixer with the hook attachment), then mix in the eggs and vanilla extract and slowly pour the milk in little by little until the dough looks cohesive (you may need less or more milk, as some flours soak up more liquid than others). Keep beating the mixture for about 7 minutes at medium speed. Add a little more flour around the inside of the bowl (2-3 tablespoons), just enough for the dough to separate from the container. The dough should be soft and slightly sticky.
YOUR DOUGH SHOULD FEEL VERY SOFT AND ELASTIC.
Place the dough on your floured working table and knead it just enough to shape it into a ball.
Place this ball in a large greased bowl to rest. Cover it with a plastic wrap (or wax paper) and a kitchen napkin. Let the dough rest in a warm place for about 2 hours until it doubles in size. I usually turn the light on in my oven and place the bowl inside, close to the light. Be aware that if your kitchen is cold, the dough will take longer to rise. Be patient and do not try to proceed to the next step until the mixture has doubled in size.