This 2021 human clinical trial evaluated sulforaphane’s cosmetic effects:

“We demonstrated that sulforaphane has the potential to become a highly effective functional hair cosmetic to relieve hair loss with androgen alopecia. Sulforaphane increases expression of the dihydrotestosterone (DHT)-degrading enzyme 3α-hydroxysteroid dehydrogenase (3α-HSD) in the liver, which accelerates DHT degradation, thereby inhibiting hair loss.

We performed a visual evaluation of parietal and frontal lines of 23 men and women from 18 to 54 years old before and after using the product, and then calculated total number of hairs. This clinical study showed that parietal lines and bangs visually improved, and the number of hairs increased by 6.71% from before using the test product to 18 weeks after using the test product.

We tested expression levels of Ak1c21 and Dhrs9 isoforms of 3α-HSD in the in vitro cell culture experiment where Hepa1c1c7 cells were treated with sulforaphane or a mixture of biotin, dexpanthenol, and l-menthol. This study showed that sulforaphane alone achieved a hair loss-relieving effect in our experimental cell culture conditions.

Our finding that sulforaphane induces Akr1c2 in a dose-dependent manner is consistent with previous studies. Sulforaphane treatment induced expression of Dhrs9, which has several sites in the promoter region that bind to Nrf2, which is induced by sulforaphane.

It is highly likely that sulforaphane might enhance degradation of DHT, not only via the induction of degrading enzymes 3α-HSD, but also by functional activation of these enzymes. Further studies remain to test this possibility.”

https://www.mdpi.com/2079-9284/8/3/63/htm “Sulforaphane, L-Menthol, and Dexpanthenol as a Novel Active Cosmetic Ingredient Composition for Relieving Hair Loss Symptoms”