Oh boy, haha. First of all, don't listen to the people who said that you can't eat a bagel and hot chocolate for breakfast. It is pure carbs, but we can stuff like that just as well as a normal person can. :/
Since you are on a pump, my first thoughts were basal, carb ratio, and sites. So, in terms of basal, have you done any basal testing lately? This could be the cause of your problem. If your morning basals are off, you could be going higher because of that. You could actually be giving the right amount of insulin and it's just not taking. That being said, you were still high after a correction dosage, so this is just something to consider.
In terms of your carb ratio, maybe you should try upping it by a carb or two in the mornings? For example, if you're on a 1u:10g ratio in the morning, try a 1u:6g. That might be what you need to bust the carbs for breakfast. You'd want to go back to your normal ratio for lunch and dinner, though.
The site could also be the problem. If you are using something like mios or insets, those have been causing quite a few people problems in the diabetes community. They tend to kink and disturb the flow of insulin. I use silhouettes and have never had this problem, but I figured that I'd inform you just in case.
On top of all this, have you checked your insulin sensitivity factor lately? In short, how much one unit of insulin will bring your bg down? If you are going high in the mornings, you may need a different ISF at that time of the day.
It's really a guess and check sort of situation. If I were you, I would eat the same thing for breakfast for a little while and mess with things until something works. That's what diabetes is all about, learning what works for you, right? (:
OH! And if you can get your hands on a CGMS, that might give you some more information in terms of where, exactly, you are spiking so that you can alter basals and other things accordingly.
Feel free to email me if you have any problems! I'd love to help you out! firstname.lastname@example.org
16 year old type one diabetic; diabetic for 11 years currently pumping with minimed paradigm using novolog. Working on obtaining CGMS.