。
She knows absolutely nothing about cooking.
Literal
She [topic-は] cooking [possessive-の] thing [contrast-は] completely does-not-know.
~のことは全く知らない means 'knows absolutely nothing about X.' のこと softens the directness by adding 'matters of/things about.' 全く (まったく, 'completely, utterly') with a negative predicate creates emphatic negation. The contrastive は after こと implies 'as for cooking specifically.'