I think that's an advanced/difficult question.
In summary I think it's recommended that you to avoid becoming 'attached' to sensual pleasure[s]. Seeking (sensual) pleasure (i.e. 'thirsting' or 'craving' for pleasure) might be a symptom of and a precursor to being attached to it. And 'contact' with objects, from which arise 'feelings' of pleasure, might lead to 'craving' and 'attachment'.
I think the above is part of the theory of the Twelve Nidānas (sense base -> contact -> feeling -> craving -> attachment).
I'm not sure but maybe theoretically you can break the chain anywhere: if you avoid contact for example then it doesn't arise; or if you have contact but avoid feeling; or etc.
Food is a difficult subject partly because (unlike sex, drugs, music, money) it isn't possible to avoid contact.
I guess that to the extent that monastics eat what they're given, they don't choose it and so it's easier to see it as uncontrolled/non-self/impermanent -- not a karmic act maybe (not an act of will) -- nothing to worry about (though this about "not worrying" is more-or-less idealistic on my part -- in practice they cope with hunger).
Another reason why I assume that this topic is difficult is because, according to the Four stages of enlightenment, "freedom from sensual desire" is associated with one of the last two stages.
Here is an annotated version of the Sekha Sutta (which Saptha Visuddhi's answer recommended). It begins to explain terms like "one whose sense-doors are guarded". Even so it might require more to understand, for example it says "he grasps neither its sign nor its detail" which supposes you understand the word "sign" (which is annotated in a footnote but also mentioned in the introduction to this Sutta Discovery essay).
It's possible that you'll find basic teaching helpful: "Thinking about food but don't get attached to the thought, let it go, keep breathing" or "This is the arising of stress, and the cessation of stress" or "Not me or mine" etc.
You mentioned "mortification" but, in English anyway, I think that means literally "putting to death" i.e. it's an extreme. Foregoing a useless snack isn't necessarily it. I think the theory is that by avoiding attachment/craving for sensual pleasure you can avoid suffering and find a more lasting ease. Mortification is wrong but (for monks, more or less 'advanced') something like disillusionment/revulsion (Nibbidā) is recommended in various of the Pali suttas.