For the dough, cream butter and granulated sugar with a mixer until pale and fluffy. Add yolks and vanilla, and beat for 1 minute. Reduce speed to low, and beat in flour and salt until combined. Cover, and refrigerate until firm, about 1 hour.

Place a rack in the middle of the oven and preheat to 325 degrees F. For the filling, whisk granulated sugar, flour, and eggs in a medium bowl. Stir in lime zest and juice and salt.

Roll balls using 2 teaspoons dough for each. Place 1 inch apart on parchment-lined baking sheets. With the handle of a wooden spoon, press gently in the center of each to create an indentation. Bake for 10 minutes. Press centers if indentations lose definition. Spoon filling into centers. Bake until cookies are light brown around edges, 6 to 8 minutes. Let cool on wire racks.