He later played for the Southland Sharks in the New Zealand National Basketball League, where he won NZNBL championships in 2013 and 2015.
Braswell was born and raised in Baltimore, Maryland, where he attended Lake Clifton Eastern High School.
His 1,569 field goal attempts were more than all but two players in school history (Eric Floyd and Reggie Williams).
[4][8] Braswell began his professional career splitting the 2002–03 season in Belgium with Tournai Estaimpuis and in Poland with Spójnia Stargard Szczeciński.
[11] He subsequently returned to Europe and played seven games for Greek team Kolossos Rodou before leaving in December 2005.
[9] In the 2009–10 season, Braswell began with playing eight games in Israel with Barak Netanya between October 25 and December 14.
[13] Following the conclusion of the Breakers' season, Braswell returned to Europe and joined French team Limoges CSP.
[20] He received interest from several other Australian NBL clubs, but a contract failed to materialise, which saw him sign with the Sharks for the 2012 season.
[22][23] Braswell returned to the Southland Sharks for the 2013 New Zealand NBL season[24] and helped lead them to the championship.
[32] On August 3, 2015, Braswell was appointed head coach of the Wellington Saints for the 2016 New Zealand NBL season.
[33][34] On April 15, 2016, he came out of retirement for a one-game stint, helping his depleted Saints in a 97–72 loss to the Canterbury Rams.
[37] In 2017, Braswell guided the Saints to back-to-back titles behind an undefeated 20–0 campaign and New Zealand NBL Coach of the Year honours.