In a pan, mix tapioca and milk on medium high heat, and stir it until boiling.
Simmer 5 minutes, uncovered at the lowest possible heat, adding sugar gradually.
Return eggs to pan with tapioca, and then boil the mixture and stirring it constantly.
Reduce heat and stir several minutes at a low simmer, stirring constantly until nice thick pudding consistency.
Cool 15 minutes. Add vanilla.