This points to an interesting feature that appears in English: phrasal verbs. This is where a verb is made up of a verb word used in combination with one or more prepositions or "particles". For example in the phrase "put cheese on the pizza" the verb word "put" combines with the preposition "on". (There is no particle in this example.) Even though the words "put" and "on" are not consecutive, and even though "on" has its own function as a preposition, "put on" together form a verb that is lexically distinct (has different meaning and rules) from "put" used with a different preposition or particle.

IIUC you even get a different meaning if you use the same words with a different function. With "on" as a preposition you get, "put cheese on the pizza". But with the particle form of "on" you get a different verb with a different meaning: "put on a coat".

The use you posted, "put cheese", looks like a transitive form of "put" which would be distinct from both of the phrasal verbs I described. My guess is that this is dialect-specific: maybe some English speakers perceive transitive "put" as valid, while others only use "put" as part of a phrasal verb.

Language is messy, and there is no authoritative set of rules for English so you'll find lots of cases where people disagree about correct grammar. One of the classics is whether "where" substitutes for a prepositional or a noun phrase. Lots of people feel it is correct to say, "Where is that at?" while others think that sounds wrong, like saying, "It's at by the corner." (I think this might be the basis for the made-up rule, "don't end sentences with a preposition".)