I get those too. Thanks for asking that question, its good to finally know what causes those white chunks to appear.
Your tonsils have crypts (like deep craters) that trap food and debris. This debris then decompses and thus can be foul smelling and tasting. When it builds up to a certain point, or you apply pressure to the tonsil, the "tonsiliths" break off.
The only way to "cure" this is to have the tonsils removed (which can be a very unpleasant surgery to have as an adult). Gargling after every meal may help to prevent the debris from depositing in the tonsilar crypts.
Good luck,
JMK MD