If I understand well : to prepare a meal - to cook -cuisiner -kuiri (as you said) and to make sth not raw (to bake ?) - cuire- kuiriĝi (or baki perhaps ?) . So many words so close..:)
The a-ending is only for adjectives. The e-ending is for adverbs. So if the adjective/adverb describes a noun like in 'The house is red.' or 'The blue monkey' then the ending is '-a'. If it describes how the action of a verb is like in: 'He runs strangely' or 'She screams loudly.', the ending is '-e'. In English the ending would be most of the time '-ly' then. When that comes, it is very probable that '-e' comes in Esperanto.