Plum Cake "Tatin"

I don't have a TV, so I don't normally get to watch the Food Network. But when I was at a math conference in Connecticut, I got to see a couple entire episodes of Barefoot Contessa. She made this cake in one of them. It is my understanding that a tarte tatin is a caramelized apple tart baked with the crust on the bottom. This has cake instead of pie crust and plums instead of apples, but it's the same idea. My pictures aren't good, but this recipe is. The fruit, which cooks on the bottom of the pan, is sweet and moist and infused with caramel flavor. If I were to do one thing differently, I would squeeze more plums in the bottom because they are the highlight of the dish. There is a good chance that visitors to my house will get this for dessert. I also plan to try it with different fruit. I think apricots would be fantastic. If anyone ever has an Iron Chef: Plum party, I will win every prize.

Plum Cake "Tatin" by Ina Garten
6 tbsp unsalted butter, room temperature, plus extra for greasing the pan
10-12 plums, preferably "prune" plums, cut in half and pitted
1 3/4 cups white sugar, divided (1 cup plus 3/4 cup)
2 large eggs
1/3 cup sour cream
1/2 tsp grated lemon zest
1/2 tsp vanilla extract
1 cup plus 2 tbsp all-purpose flour
1/2 tsp baking powder
1/4 tsp salt
Confectioner's sugar for dusting, optional

Grease a 9-inch pie or tart pan generously with butter. Place plums, cut-side down, in the bottom. Combine 1 cup sugar and 1/3 cup water in a small saucepan. Cook over high heat until sugar is 360 F. It should be a warm amber color. As tempting as it is, don't stir the pan. Just swirl it gently. Pour evenly over plums. It will bubble and hiss and eventually harden. Don't worry. It will turn liquid again when you bake it. It should look like this:
While the caramel is setting, combine butter and 3/4 cup sugar in a medium mixing bowl and cream until light and fluffy. Beat in the eggs, one at a time. Add the sour cream, zest, and vanilla and mix until combined. Add the flour, baking powder, and salt. Stir until just mixed. Pour the batter into the pan and bake at 350 F, until a tester inserted in the center comes out clean. Let cool 15 minutes if you can stand it. Then invert onto a cake dish. If a plum sticks to the pan, gently cajole it out and replace in the top of the cake. Sprinkle with confectioner's sugar if you want.