It should be the cook.
As the cook said he was cooking and the gardener said he was picking vegetables.
Now either of the two were lying since if the cook had started cooking then why the gardener was picking vegetables.
And if the gardener was picking vegetables, then what was the cook cooking.
Also, as the wife was sleeping (generally people take nap post lunch), means that she had taken lunch and the cook had already cooked...
Hence, the cook
But lot of assumptions .... family eating only garden fresh ... wife taking nap post lunch .... etc.
Kavita