Combine finely crushed graham cracker crumbs and sugar in a mixing bowl, then pour in the melted butter. Mix until the crumbs are evenly coated and the mixture feels like damp sand.
Press the crumb mixture firmly into the bottom and up the sides of a 9-inch pie dish to form an even crust. Use the back of a spoon or a glass to smooth and compact it.
Bake the crust in a preheated oven at 350°F (175°C) for about 8-10 minutes until fragrant and lightly golden. Remove and let it cool completely on a wire rack.
In a mixing bowl, whisk the egg yolks vigorously until smooth and slightly thickened, about 1-2 minutes. This helps create a silky filling.
Gradually add the sweetened condensed milk to the yolks, whisking constantly to combine fully and achieve a smooth, creamy consistency.
Stir in the fresh key lime juice, lime zest, and vanilla extract. Whisk until the mixture is uniformly bright green and smooth, with no lumps.
Pour the lime filling into the cooled crust, spreading it evenly with a spatula. The filling should look glossy and vibrant.
Chill the pie in the refrigerator for at least 4 hours, or until the filling is set and slightly jiggly in the center. This allows the flavors to meld and the filling to firm up.
Once chilled and set, slice the pie with a sharp knife, revealing the smooth, tart lime filling beneath the crisp crust. Serve cold and enjoy the bright, creamy flavor.