In a food processor, pulse together flour, cocoa, sugar, and salt. Add butter, and pulse until the butter is cut into small chunks and the dough is starting to come together. Add the half-and-half and continue to pulse until dough is almost completely together.
Empty into a 9-inch tart pan and press evenly into the pan. Prick with a fork all over, then put in the freezer for 30 minutes.
Bake for 15 minutes. Let cool while you make the filling.
To make the filling, whisk together sugar and eggs until well combined. Gradually whisk in lime zest and juice, then pour into a saucepan.
Add the butter and cook over medium heat, stirring constantly until butter is melted and mixture has thickened. This will take about 5 minutes.
Pour filling into crust and chill for at least an hour before serving.