Fill and bake the tart
In a large bowl, whisk together the eggs, sugar, and lime zest and juice until smooth, about 1 minute. Whisk in the flour and then the cream until blended. Pour the filling into the partially baked crust. Bake until the filling is set when you gently shake the pan, about 30 minutes. Transfer to a wire rack and let stand until the top feels cool to the touch, about 1 hour. Remove the tart from the pan. Cover and refrigerate for at least 3 hours or up to overnight. To serve, cut the tart into wedges and serve with whipped cream, if desired.