Now that I'm a bit more into the Korean language I've noticed that some verbs that have 고 in the middle are separated there. For instance, I've seen 보고싶다 used like 보고 싶다 or 보고 싶어.
I was wondering, what's the explanation of this?
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This doesn't directly answer your question but I add it here so you could ease up a bit when dealing with separation rules in Korean.
While there are plenty of separation rules in modern Korean grammar, you must know that Korean language is not originally designed to have separations unlike English or other European languages.
Korean language did not have separation rules until very recently and therefore native Koreans always write Korean sentences with wrong separation rules and even the rule itself changes frequently.
There definitely are some of the rules that stay the same overall (ex: you must always have separation after 'noun + ~가/이') but other rules are really just random (ex: while "보고 싶다" is a correct & recommended modern Korean separation, natives use "보고싶다" all the time).
Why do we need spaces for the Korean language? I think that spaces should be used to avoid ambiguity. Thorough separation may be advisable; however, I would say no to the question: "Can 보고싶다 ever be read as 보 고싶다 or 보고싶 다?" In this case, it seems unnecessary to put spaces although the rules say that we should write it as 보고 싶다(The rules we cover online are usually South Korean. North Korean rules will say that 보고싶다 is correct).
You can take -고 as a connector between the main verb 보다 and the auxiliary adjective 싶다; the exact term for -고 is a connective ending. Depending on the connector, the meaning of 싶다 varies. When you express your desire using 싶다, the ending of the main verb must be -고. In other words, -고 is always required for 싶다 to have that exact meaning. People do not (have to) interpret such a phrase word by word. In addition, there is -고프다, which is short for -고 싶다. As I said above, there will be no misunderstanding if you put no spaces between 보고 and 싶다. Thus, it is natural that a lot of Koreans do not separate 보고 from 싶다 in writing because they do not feel the need to put a space between those words.
Other information irrelevant to your question:
Because 보다 is a transitive verb here and 싶다 is an auxiliary adjective, 보고 싶다 is an adjectival phrase which can have a direct object. -고 싶다 is special; you can use the marker 이/가 (in place of 을/를/ㄹ) to emphasize the object when the main verb is transitive. I suppose you have seen not only 널 보고 싶어 but also 네가 보고 싶어. Both of these are grammatically correct.
The reason I have said here above is that 보다 is an auxiliary verb or adjective in some other phrases (for example, 하고 보니, 먹고 보자, and 살고 보면). That is also when -고 is used.