Preheat the oven to 350°F (175°C). Line two large baking sheets with parchment paper.
In a large mixing bowl, whisk together the melted butter, granulated sugar, and brown sugar until smooth and combined.
Add the eggs one at a time, whisking well after each addition. Stir in the vanilla extract.
In a separate bowl, sift together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Divide the dough evenly between the two prepared baking sheets. Using a spatula, spread the dough very thinly and evenly across each sheet, aiming for about 1/8 inch thickness.
Bake in the preheated oven for 18 to 20 minutes, or until the edges are golden brown and the center is set and crispy.
Remove from the oven and allow the cookie brittle to cool completely on the baking sheets. The cookie will harden further as it cools.
Once cooled, break the cookie brittle into pieces and serve or store.