Preheat the oven to 350°F (175°C). Line an 8×8-inch pan with parchment paper, leaving extra paper on the sides for easy removal later.
In a mixing bowl, combine the flour, sugar, and salt. Stir well so everything is evenly mixed. Add the melted butter and mix until a soft dough forms that holds together when pressed.
Transfer the dough into the prepared pan. Press it firmly and evenly across the bottom using your hands or the back of a spoon. Make sure the corners are filled and the surface is level.
Bake the crust for 15 to 18 minutes until it looks lightly golden and set. Remove from the oven and let it cool slightly.
In a separate bowl, whisk the egg yolks until smooth and slightly lighter in color.
Add the sweetened condensed milk and whisk until fully combined and creamy. Slowly add the key lime juice while mixing. Stir in the lime zest and mix until smooth.
Pour the filling over the warm crust. Use a spatula to gently spread it into an even layer, making sure it reaches all edges.
Bake again for 15 to 18 minutes. The edges should be set, and the center should still have a slight jiggle.
Remove from the oven and let the bars cool completely at room temperature.
Place the pan in the refrigerator and chill for at least 2 hours until fully set.
Lift the bars out using the parchment paper. Place on a flat surface and cut into squares with a sharp knife. Clean the knife between cuts for neat slices.