For the Tart Shell: Preheat oven to 375 degrees F.
In a medium bowl, mix the 3 1/3 cups coconut, egg whites, confectioners' sugar, and vanilla together. Lightly press this macaroon mixture against the sides and bottom of a buttered 9-inch tart pan to form the walls of the tart.
Bake the shell until the bottom crust is tanned and the sides are golden brown, about 10 minutes. Let cool on a rack. Lower oven temperature to 325 degrees F.
For the Orange Filling: While the shell is cooling, in a medium bowl, mix the yolks, sweetened condensed milk, extract, oil, orange juice, and zest together. Pour the filling into the cooled shell and bake until just set, about 15 minutes. Set on a rack to cool, then refrigerate until chilled.