What it means
Let him cook is a cheer to leave someone alone while they do their thing, trusting that something good is on the way even if it looks messy mid-process. You step back, stop interrupting, and let the talent work the magic.
Usage examples
"Stop backseat gaming and let him cook, he knows this level."
"The intern had a wild idea so the boss just said let her cook."
"You lot were clowning his transfer pick, then he dropped a masterclass. Let him cook."
"Bro's halfway through the redesign and it looks cursed right now, but let him cook."
Where it comes from
This one blew up online in the late 2010s and really took off in sports talk, gaming, rap chatter, and meme culture. It builds on cook meaning to do your thing brilliantly or put something together that's about to hit. Let him cook became the crowd chant version, basically saying quit meddling and trust the process.