An increase of 2 does suggest that your body is managing to cope with the carbohydrate in your one slice of bread (if that's with an egg then the fat and protein may also be helping to slow your digestion of the carbohydrates).
The general guidance is to aim for an increase of no more than 3 from a meal. As your weight comes down, and you keep those rises under control, you should see those starting numbers begin to drop under 7 as well, but it may take a while to do that.
I tend to have eggs in some form for breakfast, sometimes just 2 eggs scrambled, but I also often make a "frittata" or "crustless quiche" with vegetables and/or meat, eggs and milk and cut it up into portions - usually that ends up with about 1 egg per portion and about 2-300 calories depending on whether it's just vegetables or if I'm using up some fattier meat like salami. (I'm using carbohydrate levels and calories myself, so have no idea where it would be in terms of SW allowances/syns)