Preheat oven to 350 degrees F and grease a 9×13-inch baking dish.
Pick up two sheets of phyllo dough at a time and crinkle them in accordion folds. Fit folded dough into the prepared baking dish and repeat the process until you’ve worked through both rolls of dough. Fluff folds to ensure they’re evenly spaced.
Bake folded dough for 10 minutes.
Remove dough from oven and drizzle melted butter over the top. Return to oven and bake for 10 more minutes.
As the buttered dough bakes, whisk together the milk eggs, sugar, vanilla, almond extract, and cardamom in a medium sized bowl (a bowl with a pour spout is ideal!).
Remove the baked dough from the oven and pour the custard evenly over the top.
Bake for an additional 30-35 minutes until golden.
During the final bake time prepare the syrup. Add sugar and water to a small saucepan over medium heat. Whisking often, continue simmering until mixture thickens, about 10 minutes. Remove from heat and stir in vanilla.
Drizzle the syrup over the baked cake then let cool before slicing.