That's because 'corn' is uncountable (a mass noun), so whether you mean one stalk or many stalks of corn, you must use the singular "corn". Likewise, "verdura" in Italian counts as one individual vegetable or many vegetables.
However, you would say, "My cabbages grow over there in the field" if you meant more than one cabbage, or, "My vegetables grow over there in that field" if you meant more than one vegetable.
In my understanding, "verdura" is in fact a mass noun meaning something onv the lines of "greenery" (verd-). This appears to be a common construct in the languages I am familiar with. I'd imagine the synonym "ortaggio" would be used for a single vegetable. Native speakers please confirm though!
I agree, although "The greens grow" does make sense in English (but I wouldn't translate "greens" with "verdura"). Especially in the American South, greens refers to a variety of leafy vegetables (never referred to as green) and includes such things as turnip greens, kale, collards, etc. Greens are cooked a bit like one would cook rapini in Italian cuisine.
Actually, to say "My cabbage grows over there in the field" would also be correct, because you're referring to the plant type, not an individual plant... but "My cabbages" would explicitly indicate multiple plants of the cabbage type.
I'm sure you probably realize that, just commenting for non-native English speakers that may find this confusing.
Every language has little quirks and exceptions and so forth that you have to learn, in this case 'la verdura' (and in fact la frutta) are used to refer to vegetables in general (and fruit for frutta) instead of a single vegetable. The 'why' of it may be lost in the mists of time, or known to language specialists, for now it's just easier for you to remember that's how it is done.
In fact it may be easier for you to think of it with fruit since we treat fruit that way. We don't say "I'm going to buy fruit' and mean only a single fruit. I think the term is 'mass noun' https://en.wikipedia.org/wiki/Mass_noun
Why should they? That's a lot of work for them and there are already many Italian dictionaries out there. If you can't google them yourself try https://www.collinsdictionary.com/dictionary/italian-english/
ortaggio/ortaggi, if you want plural :) „La verdura“ is formally singular working as an uncountable (like „bread“, „fish“ and „fruit“ in Eng). An example phrase from a dictionary is: Bisognerebbe mangiare molta verdura per restare in forma. You have to eat a lot of vegetables to stay in shape.
The tips in the dropdown don't have much in the way of context, so it's best to consult a dictionary if you have an issue there. Crescere does indeed mean to grow as well as to increase depending on context. In fact there are other questions where it means to grow with regard to people, especially children. You are far more likely to encounter phrases about vegetables growing than them increasing.