D'Aste's early racing career included competition on motorcycles and in the Monza International Rally.
In 2005, D'Aste competed for Proteam Motorsport in a BMW 320i in the WTCC, finishing third in the Independents' Trophy. His best overall result that season was second in the second race at Spa-Francorchamps. He continued with Proteam in 2006, again finishing third in the Independents' Trophy, with a best overall finish of tenth.
For the 2007 season, D'Aste moved to the Wiechers-Sport team, driving a BMW 320si. He won the Yokohama World Independents Trophy that year, with his best overall finish again being tenth. He was awarded the gold helmet, an important award in a racing driver's career.
In 2008, D'Aste returned to Proteam Motorsport for his third season with the team. He finished third in the Independents' standings, failing to retain his title. He chose not to attend the final rounds in Macau, protesting a five-place grid penalty received after an incident at the previous round in Japan. This decision was made despite being in contention to prevent his teammate Sergio Hernández from winning the title.
D'Aste was initially slated to continue with Proteam in 2009, but the deal fell through, leading him to return to Wiechers-Sport. He finished the season nineteenth in the drivers' standings, with a best result of sixth at the Race of Germany.
In 2010, D'Aste began a third stint with Proteam. He again missed the season finale at Macau to attend the Monza Rally Show, even though he was still in contention for the Independents' Trophy. This left his teammate Hernández as Proteam's sole title challenger. D'Aste finished sixth in the Independents' Trophy and nineteenth in the overall standings, with a best finish of ninth at the 2010 FIA WTCC Race of the Czech Republic. At the Rally of Monza, driving a Lotus Exige GT Rally for PB Racing Team, he achieved a fourth-place overall finish and was first among GT Cars.
D'Aste returned to the WTCC mid-season in 2011, joining Wiechers-Sport from the sixth round in Portugal as a replacement for Urs Sonderegger. In his first outing under the new qualifying rules, he qualified tenth and benefited from the race two reversed grid pole position. He scored the team's first point of the season in race one but finished outside the points in the second race. He missed the subsequent WTCC round to compete in the GT4 European Cup, driving an Official Lotus Evora for Gianni Giudici's team, where he finished third in the series. He later returned for the WTCC rounds at Oschersleben and Valencia. Despite competing in only three events, he finished the season 17th in the overall standings, marking his best WTCC finish at that point.
After selected appearances in 2011, D'Aste returned to Wiechers-Sport for a full season in 2012. He secured his first overall WTCC win at the Salzburgring, where punctures for front-wheel-drive cars allowed him to overtake race leader Robert Huff on the final corner. For the fourth time in 2012, he started from reversed grid pole at Suzuka, leading from start to finish to claim his second win of the season ahead of independent rival Pepe Oriola and Gabriele Tarquini. D'Aste achieved another podium finish at the Race of China, placing third behind Chevrolet drivers Huff and Menu in race one. In race two, he ran as high as second, but his car's driver's door became stuck open, causing him to drop down the order. He arrived at the Race of Macau in contention for the Yokohama Trophy, 15 points behind leader Norbert Michelisz. He qualified behind both his rivals and was involved in a pileup at Lisboa corner on the first lap, which severely damaged his car and led to his retirement on lap two. Another accident in race two meant he scored no points from the event, finishing third in the Yokohama Trophy. However, 2012 marked his best overall championship placing, with seventh place.
In 2012, D'Aste also participated in the first edition of the Rally of Sebino, driving a Lotus Exige GT Rally. He was the first driver to win an overall race with a two-wheel-drive Lotus Exige, competing against S2000 four-wheel-drive and WRC cars.
D'Aste established his own team, PB Racing, for the 2013 season, driving a BMW 320 TC. In the first race of the Race of Italy, he crashed out on lap four, spinning on the exit of Ascari, hitting the barriers, skating across the track, and hitting the barriers on the other side before stopping. He started race two from the back of the grid and finished ninth.