Prepare the apples as stated above: Peel and then cut each apple in half. Take a paring knife and cut a half moon/u shape towards you for each half, cutting out the hard portion/core. If apples are too big, slice into quarters after coring.
In the cast iron pan (or pan with higher sides), add the butter and sugar (gently pour into the butter) together once pan is on a medium-high heat.
Incorporate the sugar and butter and then LEAVE ALONE. Mixture will slowly bubble and darken. It makes for a better caramel if you do not stir during this process, which can take anywhere from 5-10 minutes.
Once caramel is Almost your desired color, remove from the heat, stir, and drop in your apples, placing them carefully, core side facing down. You can place in a flower pattern, using one or a few smaller pieces for the center, and/or add in a few thinner pieces if you need to fill in any gaps. It does not have to be picture perfect. The Tatin will take care of itself. Add a pinch of salt over the apples.
Put the pan back on higher/high heat and cook the apples for another 10-15 minutes or so, making sure to turn the apples over twice--once to coat the other side, and again to ensure that the rounder outer sides are facing up.
Take the dough out of the refrigerator for a few minutes prior to this point and place the dough over the apples in the pan, tucking in the outer edges around the outer edge of apples. You can make a small air hole in the center.
Give pan a shake and make sure the caramel is evenly distributed, moving the pan into the oven at 375 degrees. Cook for 35-40 minutes, or until crust is golden brown. The juices will rise around the edges very soon in the baking process.
Let cool for at least 10 minutes, and, ever so carefully, place a large flat plate/platter on top of the pan. Hold with a kitchen towel or oven mits, along with the handle, and flip (with a prayer). Slowly, raise up the pan from the Tarte Tatin, giving it an extra shake if necessary.
Allow the tart to cool further, and enjoy room temperature or warm. There is no law in my land about ice cream, creme fraiche, or whipped cream on top, but I honestly think the Tarte Tatin on its very own is one of the most delightful creations for any Thanksgiving or Bastille Day, or Saturday in fall. Enjoy.