Brown the butter: Keep cooking the butter until it foams, then the foam starts to subside and you see golden to deep brown specks forming on the bottom of the pan. It should smell nutty and toasty, not burnt. This usually takes 4 to 6 minutes total once melted, depending on your stove and pan. As soon as the milk solids turn a deep golden brown, remove the pan from the heat to stop the cooking.
Combine cauliflower and brown butter: Transfer the hot, tender cauliflower to a wide serving bowl or shallow dish. Immediately pour the warm brown butter over the florets, making sure to scrape in all the toasty brown bits from the bottom of the pan.
Season and toss: Sprinkle the coarse sea salt evenly over the cauliflower. Gently toss until every piece is coated in the glossy brown butter and the salt is distributed. Taste and add a pinch more salt if needed.
Serve: Spoon the cauliflower and all the buttery pan juices onto a serving plate or individual plates. Serve right away while it’s hot, tender, and almost melting in your mouth.