I am proposing that Willem Gerritsen & Mary (both NNS PPPs) be added as the parents of Cornelis Willemse. This relationship is mentioned in two NYGBR articles and on the Brouwer Genealogical Database (BGD) website (note: the BGD cites the two NYGBR articles as its source). The citations for the two articles are:
Garretson, Aline L. “The Gerritsen-Willemsen Family Record, and The Willemson Family of Gravesend”, New York Genealogical & Biographical Record, v. 133, no. 3 (July 2002), pp. 164, 167, 170.
Hatcher, Patricia Law, ed., “Jan Brouwer of Flatlands and Descendants”, New York Genealogical and Biographical Record, v. 138, no. 4 (Oct. 2007), p. 252