Brobbel started his career with the youth system of Middlesbrough and signed a three-year professional contract with the club on 1 May 2011 after finishing his apprenticeship.[4][5] He joined League Two club York City on 30 August 2013 on a one-month loan,[6] making his debut the following day as a 74th-minute substitute for Ashley Chambers in a 2–1 defeat away to Exeter City.[7] Brobbel scored his first career goal in the second minute of the following match at home to Mansfield Town on 14 September 2013 with a header from six yards, although York went on to lose 2–1.[7][8] On 27 September 2013, after making three appearances and scoring one goal for York, Brobbel's loan was extended to 5 January 2014.[7][9] York opted against extending his loan when it expired,[10] having made 13 appearances and scored three goals for the club.[7] Brobbel rejoined York on 27 March 2014 on loan until the end of the 2013–14 season, following an injury to Josh Carson,[11] and made his second debut for the club two days later in a 0–0 home with Burton Albion.[7] He played in York's 1–0 home defeat to Fleetwood Town in the play-off semi-final first leg,[7] but did not play in the second leg, after which York were eliminated 1–0 on aggregate.[12] He made eight appearances and scored one goal in his second spell with York.[7]
Brobbel signed a new one-year contract with Middlesbrough in July 2014,[13] before joining League Two club Hartlepool United, his hometown club, on a one-month loan on 8 August.[14] He made his debut as a seventy-sixth-minute substitute in a 1–0 away defeat to Stevenage on 9 August 2014,[15] and having impressed the loan was extended for a second month in September.[16] Another one-month extension came in October 2014,[3] before being sent back to Middlesbrough by new Hartlepool managerPaul Murray in early November having made 17 appearances for the club.[15][17] Brobbel struggled to get into Middlesbrough's under-21 team after returning, with manager Paul Jenkins saying that Brobbel was "at a crossroads in his career".[18] He had trials with League One clubs Doncaster Rovers and Scunthorpe United, scoring two goals for Scunthorpe in a reserve-team match in April 2015.[19] He was a member of the Middlesbrough under-21 team that won the Under-21 Premier League Division 2 and North Riding Senior Cup,[20] but was released in May 2015 after a 15-year association with the club.[21][22]
Brobbel trained with Northern Premier League Premier Division club Darlington 1883 in the summer of 2015, before going on trial with Torquay United of the National League.[23] He signed for Darlington 1883, and made his debut in a 2–1 home win over Ramsbottom United on 9 September 2015.[24] He went on trial with a club in Scotland,[25] before he left Darlington in early-October 2015 making only two appearances for the club.[26] Brobbel joined Darlington's Northern Premier League Premier Division rivals Whitby Town, and debuted a 78th-minute substitute in a 0–0 away draw with Halesowen Town on 3 October 2015.[27]
On 1 February 2016, Brobbel signed for Welsh Premier League champions The New Saints.[28] Brobbel was named in the Welsh Premier League team of the year in the 2016–17 season.[29] After scoring 15 goals in 30 league games, he made the Welsh Premier League team of the year again in the 2022–23 season and signed a new two-year contract at the end of the campaign.[30]