Step 1In a bowl, combine the flour and salt. Cut the butter into half-inch pieces. Using a pastry blender or two knives, cut the butter into the flour until the butter is the size of peas. Sprinkle over the ice water, a tablespoon at a time, fluffing with a fork, until the dough sticks together when you try to form a ball. Form into a flat disk and cover with plastic wrap. Refrigerate for at least a half hour.
Step 1In a copper tarte Tatin pan or cast-iron skillet, mix the butter into the sugar with your fingers. Spread it out in an even layer over the pan. Starting at the outside, place the apple halves standing up in the butter-sugar mixture, each fitting into the next as if they were spooning. Fit as many halves as you can into the center. And don't worry about the fact that the apples are taller than the pan; they'll shrink down as they cook.
Step 2Place the pan or skillet on a burner turned to high and cook until the butter-sugar mixture bubbles up between the apples and turns a medium amber. This can take 15 to 25 minutes. Don't be afraid. The only mistake you can make is keeping the flame too low so the juice exudes from the apples before the sugar is caramelized. As the bottom of the apples soften, press down with a wooden spoon or spatula.
Step 3Heat the oven to 400 degrees.
Step 4Remove the pan from the heat and set aside to cool slightly while you roll out the pastry dough.
Step 5On a floured board, roll out the pastry to about 12 inches in diameter. Carefully place on top of the caramelized apples, trimming so there's just an inch or so as border. Tuck the border in around the apples.
Step 6Place the pan on the middle rack of the oven and bake for 35 to 40 minutes until the pastry is set and browned.
Step 7Cool the tart in the pan. Just before serving, warm the tart on the stovetop. Place a serving plate on top and invert the tart onto the plate. Serve in wedges with a big dollop of creme fraiche or crema Mexicana. (If you use crema Mexicana, add a pinch of sugar to counterbalance its tartness.)