Cream the butter and sugar on low in a stand mixer fitted with a paddle attachment.
Add the egg and mix. The butter will look curdled, but it will come together in the next step.
Add all dry ingredients in 2 additions, and mix just until combined. Remove the dough from the mixer and shape into a flat round disk that’s about 6 inches across. Wrap with plastic and refrigerate for 30-60 minutes.
If the dough chills for more than an hour, let the dough sit out for 15-20 minutes before rolling so that it is easier to work with.
To Caramelize the Peaches
Preheat oven to 375 degrees and begin making the peach filling.
Either peel the peaches with a peeler, or cook in boiling water for 1-2 minutes to remove the skins. If boiling, place the peaches in ice cold water to blanche them afterward. Remove the skins, cut in half, and then cut each half into 3 even slices. Set aside.
Add the sugar to a 10 inch metal or cast iron skillet and turn the burner on between medium and medium-low.
DO NOT stir. This can cause the sugar to crystalize. Allow the sugar to slowly melt, and swirl the caramel around as it liquifies. Once almost completely melted and dissolved, add the butter and stir. Allow to cook for a couple of minutes to ensure that there are no sugar granules left.
Remove from heat, let cool for 5 minutes, and arrange the peach slices on top. Be careful not to burn your hands, as the caramel will still be quite hot.
Return pan to medium heat, add the water, and bring to a simmer. Reduce the heat to medium low and cover the peaches with a lid to soften them for 5 minutes.
Remove the lid and let the liquid reduce until it is almost completely gone, anywhere between 15-20 minutes. Don’t stir so that the peaches stay in place.
While the liquid is reducing, roll out the dough to a 12 inch circle on a lightly floured work surface. Trim off rough edges to give the tart a prettier finish.
Remove the skillet from the stove, place the dough on top, and gently tuck in around between the edges of the peaches and the pan. Add 5 slits on top for air vents.
Place the peach tarte tatin on the middle rack of the oven and bake for 25-30 minutes, or until golden brown.
Remove from the oven and let cool for 30 minutes so that the peaches absorb more caramel and so that the liquid solidifies.
Place a serving dish on top of the pan, and flip over so that the peach tarte tatin is now upside down with the peaches are showing. (Be sure to use a towel or oven mitts to protect your hands.)
Eat warm with ice cream, whipped cream, pecans, or as is. This dessert is best eaten the same day, but it can be stored wrapped in plastic wrap for a day in the fridge. If refrigerating, bring the tart back to room temperature or warm before eating.