The Brooklyn Edison Company was formed in 1919 by the merger of two of the early power companies in the borough, the Edison Electric Illuminating Co (founded 1887) and the Kings County Electric Light and Power Co. (which operated the largest power plant in the borough, the Gold Street Plant, which began operations in 1900.) Informally, the EEICo was known as Brooklyn Edison many years earlier. In 1910 it erected a sign with 13 foot tall letters and 1,962 light bulbs that read "Brooklyn Edison Co." which could be easily seen from the Manhattan shoreline. (Brooklyn Life June 18, 1910 p.30)
The manhole covers for the new, official BE Co initially just changed the lettering in a design previously in use. The hexagonal "snowflake" design was used by several electric companies in the teens and twenties.
The Brooklyn Edison company, as were earlier Edison companies, was committed to underground distribution.
There are still quite a few covers with this design scattered about the borough, particularly in the north. This particular cover was found at Ryerson and Myrtle Aves in Fort Greene, Brooklyn.