Cut the butter into the flour until it resembles sand. You can do this by hand with a pastry cutter or even your fingers. If using a stand mixer, use the paddle and mix on low.
Add the beaten egg and milk, sugar and salt, mixing until the dough pulls together, but be sure not to over mix the mixture.
Dump the mixture onto a clean work space (not floured) and push the dough away from yourself with the palm of your hand. Repeat this 3-4 times, then pull the dough together with a bench scraper and roll into a ball.
In the pastry world, this action is called "frasier" and is meant to create a homogeneous dough without overworking it. The more you overwork the dough, the more elastic it becomes, meaning your tart shells will shrink more during cooking.
Flatten the dough into a disk, then wrap and let the dough rest in the fridge for a minimum of 30 minutes.
Meanwhile, butter and flour the tart circle and transfer it to a cookie sheet covered with parchment paper or silicone mat. I prefer parchment paper but either one gets the job done.
Lightly flour your work space and roll out the dough to a thickness of about 4mm. Alternatively, you can roll out the dough between two sheets of parchment paper. If you find that the dough is warming up too much, just pop it into the fridge for 15 minutes or so. I find it easier to work with chilled dough when lining my tart rings.
Trim the dough to the desired size. Personally, I place my tart ring on top of the dough, then trim, leaving an excess of about two fingers widths around the pan. Leaving too much excess dough makes it a lot harder to work with.
Line the tart ring, working the dough into the corners of the ring. The goal is to make 90° angles. Using a paring knife, trim the excess dough from the top of the tart ring, cutting away from yourself. Make sure that the knife is flush with the top of your tart pan, so the top edge of your shell will be even. Transfer to the fridge to chill until needed.