Using a spoon, remove enough of the interior of each apple so that the walls are about 1/2-inch thick all around, including the bottom, and there's enough of a well for the cake batter. Place the apples in a microwave-safe dish. Microwave the apples until just warm, 20 to 40 seconds, then remove and set aside.
Whisk together the flour, brown sugar, ginger, cinnamon, baking powder, milk, vegetable oil, and maple syrup in a medium bowl until just combined. Spoon or pour the batter inside the apples, leaving about 1 inch of space at the top of each. Microwave the apples in the same microwave-safe dish until the batter rises and sets, about 2 minutes 20 seconds. Dust the top edges of the apples with a little fleur-de-sel and let cool slightly, then serve with Apple Cider Caramel Sauce and vanilla ice cream.
Apple Cider Caramel Sauce:
Mix the sugar and lemon juice in a deep nonstick saucepan, place over medium heat and cover. Have a pastry brush and a small bowl of water nearby to brush the sides of the pot of any granules of sugar.
When the sugar starts to brown, swirl the pan to ensure even browning until the sugar is amber in color, 5 to 6 minutes. Pour in the apple cider -- step back, because there will be sputtering.
Add the butter. Swirl the pan to melt the butter, then add the heavy cream, cinnamon and ginger. Remove from the heat. The caramel will continue to thicken off the heat. Stir before serving. Makes 1 1/2 cups. Can be refrigerated for up to 2 weeks. Reheat gently on the stove top or in the microwave.