Tarte Tatin during the stove top caramelizing process

1/4 cup (half stick) unsalted butter
2/3 cup sugar
1/2 teaspoon cinnamon (optional)
1/4 teaspoon cardamom (optional)
8 apples, peeled, cored and quartered
Melt butter in a 10-12 inch diameter oven-proof pan with sloping sides. Add sugar
(and spices) and cook for a few minutes,
stirring occasionally, until sugar melts. Cover
the bottom of the pan with apples, cut side up,
snuggled closely together into the sugar mixture.
Double layer them, to accommodate all of the apple
quarters.
Cook slowly over medium heat about 45-55 minutes until apples become tender, but not mushy, and juices in the pan are caramelized to a golden brown, even a slightly brownish color in places. Keep an eye on the heat, so it doesn't get too hot and burn, nor too cool to stop the caramelizing process. You really don't need to stir, but I push the apples into the sugary mixture with a wooden spoon occasionally.
Preheat oven to 400 degrees. Roll out pastry sheet (or pie dough) to just under 1/4-inch thick and cut into a circle to fit over apples in pan. Tuck edge of pastry down into pan, covering apples completely. Bake about 20-25 minutes, or until crust is golden brown and puffed.
Remove tart from oven and immediately invert onto a plate, using two very thick pot holders! Grasp both plate and pan with hot pads, and turn them over together. Slowly lift the pan from the plate as the apples drop down over the pastry. You may need to tap the bottom of the pan a bit, to loosen all of the apples.
Serve warm with a dollop of whipped cream, creme fraiche or vanilla ice cream.

Pie Crust Recipe
2 cups flour
1/2 teaspoon salt
11/2 sticks unsalted butter, cut into small cubes
2 teaspoons cider vinegar
1/2 cup ice water
Mix flour and salt in a large bowl. With a pastry cutter, or fingers, crumble butter into flour until well integrated. Sprinkle cider vinegar over mixture and stir in well with a fork. Add ice-cold water, a little at a time and blend with fork until dough is moist enough to roll into a ball, but not too wet. Roll into one large ball for the pie crust and a smaller ball to use for patching your crust, or cinnamon roll ups for snacking!