Preheat the oven to 350 degrees F.
Coat a 9x13-inch baking pan with a thin coating of butter, or spray with nonstick cooking spray.
To prepare the apple filling, in a large skillet, combine the cold water, brown sugar, cornstarch, lemon juice, vanilla, cinnamon, and salt. Whisk to combine.
Set the pan over medium-high heat and bring to a simmer.
Stir in apples and simmer for 8 to 10 minutes, until the mixture thickens and the apples soften slightly, stirring frequently.
Transfer the mixture to prepared baking dish, drizzle over any sauce from the pan, and set aside.
To make the topping, in a medium bowl, combine the flour, granulated sugar, baking powder, and salt and mix to combine.
Add the half-and-half and melted butter and mix until just combined (just until the dry ingredients are blended in).
Pour the batter over the apples. It’s OK if some apple slices are peaking out.
Sprinkle the top with cinnamon.
Bake for 35 to 40 minutes, until a wooden pick inserted into the topping comes out clean.
Cool for 20 minutes before serving (this gives the sauce time to thicken).
Serve warm with vanilla ice cream and salted caramel sauce, if desired.