Toss the diced apples with the light brown sugar and the lemon juice in a large bowl and let them macerate for 30 minutes, stirring once partway through.
Scrape the apples and all of the liquid they released into a medium saucepan along with the water, butter, cinnamon, salt, nutmeg, and ginger.
Cook uncovered over medium low heat for 6 to 8 minutes, stirring occasionally, until the apples have just begun to soften but still hold their shape and still have some bite. Keep it at a gentle simmer rather than a hard boil, and do not put a lid on it at any point. Apples that are cooked past this point keep releasing liquid and start breaking down, and a hard boil drives off the juice you are trying to keep.
Whisk the cornstarch into the cold water until completely smooth. Bring the apples up to a steady simmer, still short of a rolling boil, then stir in the slurry.
Cook for 3 to 5 minutes, stirring, until the mixture is thick and glossy and the starch has lost any raw edge. Do not stop as soon as it thickens, and do not let it boil hard while it finishes.
Remove from the heat and stir in the vanilla extract.
Spread the filling in a thin even layer on a rimmed sheet pan and refrigerate until completely cold, at least 1 hour. This can be made up to 3 days ahead.