Open staircase
Beautiful staircase.
I accidentally put the answer under myself, sorry folks.
Half Landing Stairs.
Dear Corey,
Browsing the Internet, I found a couple of websites that seem to be calling this style "u-shaped." http://designedstairs.com/photo-gallery-u-shape/
Warning---this answer contains whimsical knowledge.
A good definition requires both a genus and a specific difference (Formal logic 101)
Genus: Designer
Specific difference: U-Shape.
U-shape, switchback or half turn are the names that I'm familiar with this style of stairs.