Whisk granulated sugar, brown sugar, cornstarch, apple juice or water, cinnamon, nutmeg, and allspice in a large saucepan over medium heat until the sugar dissolves. Keep whisking until the mixture looks smooth, no dry streaks remaining.

Add sliced apples and lemon juice, then stir to coat each apple slice. You should see the fruit evenly covered with the spiced mixture.

Cook over medium heat, stirring occasionally, for 10-12 minutes until the apples are tender and the sauce has thickened to a glossy syrup. Look for a syrupy sheen that clings to the apple slices.

Remove the pan from heat and stir in unsalted butter and vanilla extract until fully melted and incorporated. The filling should look glossy and evenly flavored.

Cool completely before using in a pie, or pour into sterilized jars and refrigerate up to 2 weeks. Let it cool to room temperature so the sauce sets properly.

Spoon the filling into pies, crisps, cobblers, crepes, or use as an ice cream topping. Serve once cooled for best texture.