Ebbesvik began his racing career in 2005, driving for Team JLR in the British Formula Ford Championship. He finished the year in sixth place and also took part in the end–of–season Formula Ford Festival at Brands Hatch, where he failed to finish. He continued in the series in 2006, improving to fourth place in the championship. He took four podium finishes during the season, including a win at Thruxton. He again took part in the Formula Ford Festival, this time competing in the Duratec class, but once again retired from the race.
In 2007, Ebbesvik moved up to Formula Three, competing in the Spanish championship for the British outfit Team West–Tec. He was entered into the secondary Copa de España class, which featured older–generation Dallara chassis. At the end of the season, he finished tied on points with Peruvian driver Juan Manuel Polar, but took the title by virtue of taking more second places than Polar after they scored seven class wins each. For 2008, he remained with Team West–Tec in Spanish Formula Three, beginning the year with a Dallara F306 chassis before switching to a newer F308 model after the first two rounds of the season. In August of that year, Ebbesvik dominated the most prestigious race of the season to win on the Valencia Street Circuit, with the race acting as a support event for the Formula One. He took a further race win at Jerez in October to finish the championship in tenth place, one position ahead of team–mate Jonathan Legris. Ebbesvik continued in the championship for a third year in 2009, when the series was renamed as the European F3 Open Championship. He finished the season in fifth place, taking a single victory at Donington Park with further podium places at Magny–Cours and Monza.
Ebbesvik made a full-time switch from single–seaters to sportscar racing in 2010, racing for Team Bruichladdich in the LMP2 class of the Le Mans Series and Le Mans 24 Hours, sharing a Ginetta–Zytek GZ09SB/2 with Tim Greaves and Karim Ojjeh. In the second event of the season, the Spa 1000 km, Ebbesvik was injured after an accident involving a slower GT car, sustaining a fractured vertebra which subsequently ruled him out of the following month's Le Mans 24 Hours. Two overall fifth–place finishes, including anchoring the team to its best ever podium position in LMP2, at the following two rounds in Portimão and Hungaroring ensured that he finished the year in fifth position in the LMP2 standings. Indeed, at the season finale at Silverstone, Ebbesvik managed to take the Zytek into the LMP2 lead for the first time ever, although the car was subsequently crashed by Ojjeh. Ebbesvik was due to continue with the team in 2011, competing alongside Ojjeh and team newcomer Gary Chalandon, but was surprisingly and unexpectedly replaced by Tom Kimber–Smith a few weeks before the start of the season. He did, however, sign a last–minute deal to race in the season–opening event at Paul Ricard, where he finished 10th overall in an LMP2 class Oreca 03–Judd entered by Race Performance. For the second round of the season, the Spa 1000 km, Ebbesvik was set to graduate to the premier LMP1 class, racing a Lola–Judd for the Guess Racing Europ team, but the entry was withdrawn as the car would not be ready in time for the event. For the final two rounds of the 2011 Le Mans Series, Ebbesvik signed to Boutsen Energy to lead their LMP2 campaign, replacing their previous pro driver, Nicolas de Crem, in the team's Oreca 03-Nissan.
