Position the rack in the center of your oven and preheat to 350°F. Line a 9x13" metal pan with parchment paper, set aside.
Mix together graham cracker crumbs, sugar, and brown sugar. Add the butter and stir until all crumbs are moistened. Press into the bottom of the prepared baking pan. Bake for 10 minutes, then remove from oven but leave the oven on.
In the bowl of an electric mixer with the whisk attachment, whisk egg yolks for 2 minutes. Add the condensed milk and whisk for another 2 minutes. Scrape down the sides, then add the lime zest. With the mixer on low, slowly drizzle in the lime juice, then let the mixer run on medium for 2 minutes once added. Pour into the crust and bake for 15 minutes.
Let cool to room temperature before moving to the fridge and chilling for at least 2 hours, or overnight for best results. Slice and serve chilled.