1) Preheat the oven to 350°F. Lightly grease a 9" round pan that's at least 2" deep. If the pan isn't 2" deep, use a 9" square pan, or 1 1/2-quart casserole dish. Drizzle 2 tablespoons melted butter into the pan, swirling the pan to coat the bottom.
2) To make the filling: Whisk together the sugar and cornstarch, then combine the mixture with the remaining filling ingredients. Set the filling aside.
3) To make the cake: Whisk together the eggs, sugar, melted butter, and extracts.
4) Whisk together the flour, baking powder and salt.
5) Add the flour mixture to the bowl alternately with the milk, beginning and ending with the flour and stirring thoroughly after each addition.
6) Pour the batter into the prepared pan. Sprinkle with coarse white sparkling sugar or cinnamon-sugar, if desired.
7) Spoon the peaches (with any accumulated juice) on top.
8) Bake the cobbler for 50 to 60 minutes, until the fruit is bubbling and the cake is a light golden brown.
9) Remove the cobbler from the oven, and let it cool for about 10 to 15 minutes before serving. Serve with whipped cream or ice cream, if desired. Cover any leftovers, and store at room temperature for several days. Freeze for longer storage.
Yield: 8 to 10 servings.