Kostecki's nickname originates from an incident at Norwell Motorplex in Queensland, where he was a passenger in a VT Commodore driven by his cousin Kurt when the brakes failed. Faced with an uncontrolled car travelling at approximately 110 km/h, Brodie jumped from the passenger door, slid across grass, and came to rest in a bush. He was uninjured, but the episode became part of Kostecki family motorsport lore and the nickname has followed him throughout his professional career.
Kostecki made his Supercars debut at the 2019 Bathurst 1000, sharing a car with his cousin Jake Kostecki. The pair crashed out on lap 111. They also competed at the Gold Coast and Sandown rounds that season, recording a best finish of eighth at Sandown.
In 2020, Kostecki joined Eggleston Motorsport for the COVID-shortened Dunlop Super2 Series, claiming two poles, two wins, and three fastest laps. He also co-drove with Anton De Pasquale for Erebus at the 2020 Bathurst 1000, where they finished ninth.
For 2021, Erebus signed Kostecki alongside Will Brown following the departures of David Reynolds and De Pasquale. Kostecki scored three podiums across the season at Sandown, Eastern Creek, and Bathurst, finishing ninth in the standings with 1,788 points. In 2022 he moved up to seventh in the points, adding two more podiums at Eastern Creek and The Bend.
The 2023 season was transformative. Entering with five podiums from 71 starts and no wins, Kostecki and Erebus converted sustained pace into championship results, securing both the drivers' and teams' titles — the team's first Supercars Championship.
In early 2024, weeks before the Bathurst 500, reports emerged that Kostecki had parted ways with Erebus amid internal tensions, with naming rights sponsor Coca-Cola and other partners also withdrawing. Todd Hazelwood replaced him for the opening rounds in Bathurst and Melbourne. On 7 April 2024 it was confirmed that Kostecki would return to the team from the Taupō round onwards. He subsequently moved to Dick Johnson Racing for the No. 17 Ford Mustang programme.
Kostecki made his NASCAR Cup Series debut in 2023 at the Indianapolis Motor Speedway road course, driving the No. 33 Chevrolet for Richard Childress Racing — an additional entry fielded specifically for him. He qualified eleventh and finished twenty-second. In October 2023 it was announced that Kostecki would run up to five Cup Series races in 2024 through a partnership between Erebus and Richard Childress Racing, including at least one oval event. However, in May 2024 Kostecki's long-time mentor Paul Morris confirmed the planned appearances had been cancelled.
Kostecki's 2023 championship arrived at the end of a build period that showed consistent improvement across three full seasons at Erebus. His willingness to compete internationally and his adaptability across both oval and road-course formats signal ambitions beyond the domestic Supercars grid. The circumstances surrounding his 2024 departure from Erebus, and his subsequent move to Dick Johnson Racing, represent one of the more closely watched driver transitions in recent Supercars history.