Step 1: In a large bowl, combine the peeled, cored, and sliced apples with granulated sugar, brown sugar, flour (or cornstarch), cinnamon, nutmeg, and allspice (if using). Add the lemon juice and toss gently to ensure all apple slices are evenly coated.
Step 2: Transfer the apple mixture to a large saucepan or Dutch oven. Add the melted butter (if using) and water (if needed). Cook over medium heat, stirring occasionally, for 10-15 minutes, or until the apples have softened slightly but still hold their shape, and the sauce has thickened.
Step 3: Remove the filling from the heat. Taste and adjust spices or sugar if desired. Allow the filling to cool completely before using it in a pie, crisp, or other dessert. Cooling prevents the crust from becoming soggy.
Step 4: Once cooled, the filling is ready to be used in your favorite pie crust. If not using immediately, store in an airtight container in the refrigerator.