Preheat oven to 350°. Line 2 large baking sheets with parchment.
In a large bowl, whisk condensed milk, butter, lime zest, and lime juice until incorporated.
Add cornstarch ¼ cup at a time, whisking well after each addition. Once mixture starts to thicken, form into a dough with your hands. Turn out dough out onto a surface generously dusted with cornstarch. Knead, adding more cornstarch as needed, until dough is barely moist and surface is shiny, smooth, and supple, about 5 minutes.
Wrap dough in plastic wrap and chill until firm, at least 20 minutes or up to 1 hour.
Portion dough into 2-tablespoon rounds and arrange on prepared sheets, spacing 2" apart. Flatten with a fork.
Bake cookies until tops begin to crack, 12 to 15 minutes.
Let cool completely on sheets.
