It is not entirely clear what you are asking or presupposing, especially whether you are looking for theoretical possibilities in imaginary languages, or actual counts based on English (or some other language). "Teach" is most verb-like and "teacher" is less verb-like, with "teaching" standing between the two (and potentially divisible into the forms in "I am teaching" versus "Teaching is irritating"). Is "teaching" a verb or is it not a verb? In other words, it's not clear what you mean by "verb". You have a couple answers that imply that you just need one dummy verb: actually you wouldn't need any overt thing that you'd label a verb. You wouldn't even need a verb to distinguish stative and active predicates.
All actions involve relations between things ("thing" being a non-technical term meaning "anything you want to talk about"). In English, in order to describe the act of cooking porridge, you need one verb (cook) and a noun that says what you cook. In Logoori, you need just one verb ruga and no object, because the object of the verb is implicit in selecting that particular lexical item (if you want to cook beans or leaves, you would deeka them). The English verbal lexicon is thus somewhat less more compact in not including the "cook+porridge" relationship as a distinct lexical item. So it appears that you're looking for a minimal list of lexical "verbs", shifting the burden to compositional semantics (thus all forms of cooking are "cook + object"). "Fry" would be e.g. "cook with oil", "simmer" would be "cook slowly", "blanch" would be "cook quickly in water" and so on. "Cook" would itself be decomposed into a longer description involving some verbal action plus the nouns "heat" and "food", which in many languages are simply nominalizations of verbs "eat", "be warm". If you count such potential V-to-N nominalizations as not verbs, then you could theoretically eliminate "cook".
So it depends on how you dispose of V-to-N derivations, and on whether you're asking for actual language facts or merely an imaginable scenario.