Peel, core, and thinly slice apples.
In large pot, whisk together brown sugar, cane sugar, cinnamon, cardamom, and salt.
Add apple slices and lemon juice, and toss until the apples are evenly coated in the sugar and spices. Set aside for 30 minutes to draw some of the juices out of the apples.
In small bowl, stir together cornstarch and water until smooth.
Set pot with apples over medium-low heat. Cook, stirring, until apples soften slightly - about 5 minutes.
Raise heat to medium and pour cornstarch mixture over apples. Cook, stirring, until apple juices bubble and thicken - about 30 seconds.
Remove from heat and stir in lemon zest and vanilla.
Allow filling to cool completely before using in a pie.