You could say 'I told him what had happened recently', but if you say 'many things' then you need 'that' to link with the verb. 'What' substitutes for 'many things' and does not require 'that'. You don't need to say 'of food' because it is understood that eating means food, but you can say what particular kind of food you ate a lot of. eg 'I ate a lot of sushi and . . '