Holy moly, she just got a hit on Reddit. It turns out to be “Gomphocarpus physocarpus (Apocynaceae family), commonly known as balloonplant”, or seed pods.
I tried searching the Better Homes & Gardens Plant Encyclopedia online at http://www.bhg.com/gardening/plant-dictionary/. This database has facets for searching by plant size, type, and the zipcode where the plant is found. I checked www.usps.comand used zipcode 11201 for Brooklyn, NY in my search. Unfortunately, I did not get a likely match for a 3-8 foot shrub or a tree (of any height) in Brooklyn.
I then resorted to Google and entered the search term “green plant with puffy spiky bulbs” and tentatively identified your plant as a Strawberry Bush. There was no match so I returned to the images to review their tags and then looked for a Balloon Plant and Gomphocarpus Physocarpus. Unfortunately, neither the Brooklyn Botanic GHarden or the BHG encyclopedia had entries, so I entered the scientific term into Google and found a plant description at the Missouri Botanical Garden here: http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=e373#AllImages
They describe it as a shrubby perennial that grows 4-6 feet noted for its balloon-like pods