Place an oven rack in the upper-middle position and preheat the oven to 500 degrees F.

In a large bowl, whisk together flour, granulated sugar, salt, nutmeg, and ground ginger. In a medium bowl, whisk together half-and-half, eggs, and vanilla extract. Pour the half-and-half mixture into the flour mixture and whisk until smooth, without lumps.

In a 10-inch nonstick ovenproof skillet set over medium-high heat, melt the butter. Add the apples and brown sugar. Cook, stirring frequently, until the apples are golden brown, about 10 minutes. Remove the skillet from the heat and stir in lemon juice. Pour the batter around the edges of the pan and then over top of the apples.

Place the skillet into the oven and immediately turn the heat to 425 degrees F. Bake until the pancake is brown and it has puffed above the edges of the skillet, 15 to 18 minutes. Using a rubber spatula, loosen the edges of the pancake from the skillet and invert the pancake onto a serving platter. Sift powdered sugar over the top of the pancake and cut it into wedges. Serve immediately.