OMAD means getting all your nutritional needs at that sitting. Not starvation. A few cups of carrot soup isn’t going to meet your ongoing needs and you’ll quickly become malnourished missing essential minerals vitamins and fats.
I’m not an insulin user but surely there’s more than these two options? Where are you and how do you get your insulin, maybe someone else can help with ideas how to better solve this issue.
I see you are type 2 not 1. Do you know if you still produce insulin yourself? Most of us do and it’s usually a lot, but not very effective at overcoming our resistance to it. It could be that simply cutting out the carbs rather than all food might be a better solution than no food, at least for right now.