My 2.6yo dd goes through phases of this and I really struggle to know how to best deal with it too.
The last time she was really bad it was starting to impact on everything we did so I tried (perhaps successfully) to tackle it a bit.
One day at toddler group she was pestering for food so much that I just couldn't stand it any more! I just wanted to have a 5-min conversation with my friend without being pestered for food when she had had a big snack 20 mins previously.
I told her that if she kept pestering for food I would go and put her on the other side of the room because I was trying to have a conversation.
She kept pestering so I put her on the other side of the room, returned to my friend and completed my 5-min conversation in peace. I tgen went to play with dd. And she didn't pester me again until lunchtime.
Writing it down, it does seem a little harsh but it is sooooo draining to be pestered for food all the time and I had had enough.
I think you need to get to the bottom of why she's asking all the time though. Last time for us it was all about attention as it coincided with dd2 being born.
Previously to that it has sometimes been about comfort. So if she fell over she would immediately ask for food. We spotted this and started offering copious cuddles instead.
Obviously if she's hungry we give her food but we really try to be tuned into whether there might be another reason for her asking.
That felt like a bit of a ramble but I really know what you're going through.