Non-diabetic post meal spike

That is a normal rise after a meal but since you've got the test strips why not experiment:

Test at 2 hours and 4 hours to see how far from a baseline you have travelled.
Observe which meals increase your blood glucose the most and this will give you an idea of what may be causing other health risks e.g. tummy fat or high ldl cholesterol or blood pressure problems.
Why is your girlfriend worried? There are risk factors for type 2tdiabetes which are broadly around markers such as weight, blood pressure, family history, ethnicity, waist size and age but often these things can be present for 10-15 years before blood sugar problems show up so logically it would be best to reduce risk factors that you can reduce before giving yourself a false sense of reassurance that you're not diabetic yet.
Obviously if you are also really tired, very thirsty and wee ing a lot then these are classic symptoms of actual diabetes but with the totally normal sugars mentioned then I doubt you are there yet!

One thing to bear in mind is that home testing kits are not 100% accurate.
Their accuracy is presented as a percentage - most are within 15% .
I mention this because, being a percentage, the higher the value, the further out the reading could be.
So a 12.6 could "really" be 10.7.

The other thing which may be of interest is looking at CGM graphs (continuous glucose monitors - a plot of blood sugar levels taken something like every 5 minutes) for someone without diabetes. There are a few on the internet, especially since Abbott released the Libre for athletes. This is one example - there are others. This may herlp put what you see into context.

I would not be comfortable with such a variance at any starting point. My bias is that I never spike more than 2 personally and post meal tend to stay under 6 mmol/L (saw a 6.2 with a apple experiment and had a mini melt down, so I am not representative). My point is that it is generally regarded as not desirable to go over 7.8 post meal, due to microscopic damage above that amount, and a raise of more than 2 mmol/L is said to be a spike.

I would say that based on the food mentioned, you don't get on with the type of bread used for the rolls, but that your insulin response smashes the resulting sugars into the cells well enough, the speed of which may leave you feeling hungry sooner than you should. For me, I would want to test other carbs to see the numbers on these, as there maybe some carbohyrate intolerance to certain foods.