OK, I have another variation on the Tarte Tatin recipe, which I picked up in France last year.

Advantages:
- it's Authentic(tm)!
- it's easier than the other recipes listed here so far (ok, I think it's easier, but others might not agree... it is longer but that's because I'm trying to give all necessary detail!)
- includes instructions for making a really good crust!

Tarte Tatin
There is one piece of equipment that really helps make it all work: a 8-10" cast iron or other thick walled pan with sides at least 2" high, preferably straight-sided (not very slanted), and with a metal handle so it can take the heat of a 425 degree F (220 degree C) oven. You also need thick enough oven mitts or pot holders to withstand that temperature, of course.

Ingredients:
Crust:
1 3/4 cups (200g) all-purpose flour
1/2 cup (125g) butter, diced
1 egg
2-3 Tbsp superfine sugar
1-2 Tbsp milk (optional)
pinch of salt

Filling:
1/2 cup (125g) butter, diced
2/3 cup (125g) superfine sugar
8-10 apples (about 1Kg) - in the USA types that work well include Gala and Fuji
1 Tbsp lemon juice (optional)

To Make the Crust:

- Sift flour into a bowl.
- Make a well in the center and add the butter, sugar, egg and pinch of salt.
- Work together lightly to form a dough. If too dry, add milk or water. Dough should be dry enough not to stick to hands.
- Form into a ball and chill for at least 1/2 hour.
- The next two steps may be done in advance or while the filling is cooking.
- After the dough is chilled, roll it into a circle a little larger than the size of the top of your pan. The way that I've found to work best is to use sheets of plastic wrap on each side of the dough -- this lets you avoid using extra flour and creating a mess.
- When you've rolled the dough about the right size, trim using the pan as a guide, cover with plastic wrap again, and put back in the refrigerator.

To Make the Filling:

- Cut the apples into quarters lengthwise.
- Core and peel the apples.
- You may optionally dip them in lemon juice as you cut them and peel them to avoid browning.
- Pour the sugar into the pan, covering the bottom evenly.
- Put the diced butter into the pan, also distributing it evenly.
- Alternatively you can melt the butter, turn off the heat, pour in the sugar, mix to distribute evenly, then continue.
- Place the apple quarters into the pan on their edges (cut sides), as tightly as they can fit. Place them in a circle, one end at the rim of the pan, leaving an empty spot in the middle.
- When you think you've filled up all the space, try to jam a few more pieces in.
- Now fill in the middle with as many apple quarters as you can, also on their sides.
- Now cut up the remaining apples into smaller slices and jam them in wherever you can. Some apples are larger than others, so there may be some height variation. Wherever you find this, use extra slices to top off the apples so that there's roughly the same height of apple all over the pan. The idea is to STUFF the pan with apples while creating a nice looking pattern.
- Now apply a low heat to the pan while preheating your oven to 425 degrees F (220 degrees C, Gas Mark 7).
- Cook over a burner on low heat until the apples get slightly translucent (about 35 minutes). The liquids in the pan should be bubbling for most of this time. Do NOT use a high heat during this time.
- Now increase the heat to medium. NOT high. Continue to cook until the liquid caramelizes. You can check this by carefully scraping the bottom of the pan with a butterknife stuck between the apple pieces. The very tip will have a bit of brown caramel when this stage is finished. If you get any black out, you've burned it a bit, but a slight burn won't ruin the flavor. This is the most important step of the recipe: if you don't cook long enough on a low enough flame to create an even light brown caramel, the tart won't really work!
- Turn off the burner, take the crust dough out of the refrigerator, peel off the plastic, and carefully place the crust over the apples.
- Put the pan into the oven and cook until the crust is golden brown (about 20 minutes).

To Unmold the Tarte Tatin:

- Allow to cool for 5-10 minutes.
- Check the fluidity of the mixture by tilting the pan slightly. If it's very liquid you can continue to cook it on top of the stove at low to medium heat for another 5 minutes or so.
- Shake the pan a bit to loosen the apples, put a dish over the pan, and flip it all over. Remember to be careful not to get burned if there was any liquid (you can pour off the liquid if there's too much of it, then put it back on top once the tart is unmolded). If any apples have stuck to the pan, remove them carefully with a fork and put them in their place in the tart.
- Serve warm! If you don't serve it immediately, warm in an oven before serving.

- Alternatively, you can prepare the tarte Tatin ahead of time and leave it in its pan. When it's time to serve, heat the pan on top of the stove on a low flame for 2-3 minutes until the caramel becomes loose. Shake the pan to loosen the apples and flip it over onto a dish as above. Leaving the tart to rest for a couple of hours also helps to absorb any left over fluid.