To followup this question. If let’s say I went to sleep at 9pm and woke up at 2am to work and then went back to sleep at 5am for another 2 hrs. Would I wait to say birchas haTorah at 7am when I got up for the day or would I need to say it at 2am?
When does the chiyuv for birchas hatorah start? I work transcribing Torah shiurim and sometimes I work after chatzos at night. Do I need to say birchas hatorah after chatzos or can I wait till morning?
The chiyuv of birkas hatorah starts when you start a new day. If you are continuing your day after chatzos at night you do not say birkas hatorah again, because we only say a new birkas hatorah by a new day. If however you went to sleep for the first half of the night and now you woke up for the day, then you would say birkas hatorah now
This is a tough question and I don’t have a good answer for you. I discussed your question with a big posek, and he came up with a novel idea, although he admitted that he hasn’t seen anyone that writes this idea. His idea was to say the first bracha after you wake up the first time, and you may learn even after saying one of the two brachos. Then in the morning when you wake up for the day, you will say the second bracha.