What's the term for cutting part way through a vegetable or fruit to increase surface area?
I think the term you are looking for is accordion cut. It is the technique you describe, making slices not all the way through, leaving an end or side intact. 

It is most widely known for preparation of hasselback potatoes, but can also be used for meat and other items. Please see pics below of hasselback potatoes and meat.





Other times that I have used this cut is when fine dicing celery and other veggies and, quite similar to your use, when using a block of salt meat for seasoning vegetables.