In a bowl beat the egg white with a pinch of cream of tartar until soft peaks form. Once soft peaks form, slowly stream in 1/2 c. sugar while beating continuously.Next, beat in the egg yolk.
Turn beaters off & switch to a rubber spatula. Fold in 1/3 of the flour mixture, followed by 1/2 of the half & half. Repeat until finished. Scrape this mixture into the cake pan & level it with the spatula.
In a measuring cup, stir together the 1/2 c. half-and-half & the 2/3 c. sweetened condensed milk. Using a fork, make holes all over the cake. Pour the condensed milk mixture on the cake slowly.