Position oven rack to upper-middle position and heat oven to 500 degrees F.

In a mediium bowl combine the flour, sugar and salt, mixing well. In a second medium bowl, whisk together eggs, half-and-half and vanilla. Add liquid ingredients to dry and whisk until no lumps remain, then set batter aside until needed.

Heat butter in a 10-inch ovenproof nonstick skillet (or a well seasoned 10-inch cast-iron skillet*) over medium-high heat until butter is sizzling hot. Add apples, brown sugar, and cinnamon; cook, stirring frequently, until apples are golden brown, about 10 minutes. Turn off heat and stir in lemon juice. Working quickly, pour batter evenly over apples. Place skillet in the upper-middle position of oven preheated to 500 degrees F. Immediately lower temperature to 425 degrees F. and bake until the pancake edges are browned and puffy, and have risen above edges of skillet, about 18-20 minutes.

Remove skillet from oven, loosen pancake edges with a spatula and invert pancake onto a serving platter. Dust pancake with confectioners sugar and cut into wedges to serve. If desired, the pancake can be served with warm caramel sauce, or warm melted apple jelly, or warn apple butter, or warn maple syrup, and/or a big dollop of whipped cream.

*Note: If using a cast-iron skillet, preheat oven to 425 degrees F. and when cooking the apples, cook them only until just barely golden, about 6 minutes. Cast iron retains heat better than stainless steel, making the higher oven temperature unnecessary.

To make Caramel Sauce: Place water in heavy-bottomed 2-quart saucepan. Carefully add sugar to center of pan, making sure not to let sugar crystals adhere to sides of pan. Cover and bring mixture to boil over high heat. Once boiling, uncover and continue to boil until syrup is thick and straw-colored (300 degrees F.), about 7 minutes. Reduce heat to medium and continue to cook until syrup is deep amber (350 degrees F.), about 1 to 2 minutes.

Meanwhile, bring cream and salt to simmer in small saucepan over high heat (if cream boils before sugar reaches deep amber color, remove cream from heat and cover to keep warm).

Remove sugar syrup from heat and very carefully pour about one quarter of hot cream into syrup (mixture will bubble vigorously), and let bubbling subside. Add remaining cream, vanilla, and lemon juice, whisking until smooth. Makes about 1 1/2 cups.

Sauce can be cooled and refrigerated in airtight container for up to 2 weeks. If you make the caramel sauce ahead, reheat it in the microwave or a small saucepan over low heat until warm and fluid.