Present Perfect isn't necessarily about a repeated action, MehrdadIR. It's about something being 'unfinished' (in this case the period of time). "I've only seen him once today." (Today is unfinished - action is not repeated). I've been coughing a lot this morning. (Continuous action, 'this morning' is unfinished). I've coughed a lot in the past hour. (Repeated action, 'the past hour' is unfinished) My explanation is an over-simplification of the use of Present Perfect - it's better to study it in small bits.

Mehrdad, you are completely correct in your OP — we can use the present perfect for single or multiple occurrences within the present timeframe. The word “this” is a clue that it’s part of the present timeframe, so we have phrases such as “this hour”, “this day” (i.e. “today”), “this year”, etc. Note that in colloquial American English, there is a tendency to just use the simple past in such a context, even though the present perfect is technically correct.

I can say he has broken his leg second time this year. This year is also a specific time.

Hello! In this case, because you mention "this hour", which is a specific time frame, then you would have to use the past tense: I coughed 10 times this hour.