Preheat oven to 350°F (175°C). Line a 9x13 inch baking sheet with parchment paper.
In a medium bowl, combine flour and 1/4 cup sugar. Cut in cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Press the crumb mixture into the bottom of the prepared baking sheet.
Spread the apricot jam evenly over the crust.
In a separate bowl, whisk together egg whites, 1/2 cup sugar, coconut, and vanilla extract until well combined.
Pour the coconut mixture over the jam layer.
Bake for 25-30 minutes, or until the topping is golden brown and the crust is set.
Let cool completely before cutting into bars.