Turns out it's a Fatsia Japonica.
This plant is also known as Japanese Aralia or false castor oil plant (sexy!) and it can get to eight feet tall. That sort of makes me want to remove it, but then I read this:
"In Japan, the shrub was traditionally planted on the north side of a home to help ward off bad spirits." (Source: rainyside.com)
So now I really can't remove it. What if bad spirits take up in my house? My roommate is already convinced we have a basement ghost, so who knows what could happen next! Well played, mystery plant. You can stay.
On the plus side I get to make me cookies!