What's the term for cutting part way through a vegetable or fruit to increase surface area? The other day I braised beef asian style (a bit of weak beef stock, sweet soy syrup, and dark soy sauce if you're wondering), and I put in some ginger. I wanted to keep the ginger together but give the most surface area to let its flavors out, so I cut into sticks which were still connected to the base. I was explaining to someone what I'd done, but I could not come up with a name for what I did. 

What is the name for this technique?
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.