Piastri has quickly identified himself as a star in the making with composed performances in the four races so far in 2023.
In Azerbaijan last week, he managed to stay out of the walls, unlike his two fellow rookies, and brought the MCL60 home in 11th despite battling a stomach bug.
It was the lastest in a string of similarly composed performances at the start of his top-flight career.
“We're very impressed with him,” said Brown of Piastri.
“He's very focused. He's not really made any, certainly not any big mistakes – typical exploring the limits, so the odd lock of a wheel here and there.
“Early indications are we've got a future world champion on our hands; [we] just need to work to get a faster car now.”
He then qualified well for the Saudi Arabian Grand Prix to progress through to Qualifying 3 for the first time.
A clash with Esteban Ocon at the start left him with damage to his front wing, preventing him from chasing a stronger result.
He recorded his first points in Australia after a composed performance throughout a chaotic race.
“Oscar has been impressive since we've had him in the car,” Brown observed.
“He's very mature; he's very focused; he's very technical.
“So, the combination of Lando and Oscar, I couldn't think of a better combination of drivers.
“Oscar has done a fantastic job and he's trading lap times with Lando now, and that's what you want with your drivers.”
Brown also offered insight into how badly Piastri suffered in Azerbaijan, the Australian having somewhat downplayed his condition.
“He just kind of got on with it,” the McLaren boss explained.
“The reports I was getting was we might pull him out of this session; we might pull him out of the sprint race.
“He was right on the edge and he just kind of put his head down and powered through it.
“That was very impressive because I know I can't survive on three pieces of toast over the weekend!”