Add apples, water, brown sugar, lemon juice, cinnamon, and nutmeg to a saucepan and heat over medium low. Cook covered, stirring occasionally, until apples are tender to your liking, about 5-15 minutes.
The apples should release some water as they cook down, but if your apples look too dry, you can add an extra tablespoon or two of water.
Whisk together the cornstarch and water for the slurry, then mix into the apples and stir for about 30 seconds until the liquid thickens. Turn off heat.
Serve warm or cool to room temperature, then cover and store in the fridge.
Notes
Apples: Use crisp, firm varieties like Pink Lady, Honeycrisp, Fuji, Granny Smith, etc. You can also mix and match more tart apples (like Granny Smith) with sweeter apples (like Fuji). You can peel them if you'd like but I usually don't.Sugar and Lemon Juice: You may need more or less depending on how sweet/tart your apples are, so adjust to taste.