Gentleman's Beard

The vest and trousers come off a workbench, but the beard itself is a Stylist purchase, so the set is gated behind rescuing her, not behind any boss. You only ever buy the shortest version. The two longer beards are never stocked and have to be grown on your own face.

Growth only happens while the beard sits in a real accessory slot, not a vanity one, which means giving up a working slot for something that does nothing but look good. Leave it there through a normal play session and it starts rolling to advance a stage, then rolls again for the last one, so the longest beard is patience rather than farming. Journey mode time controls do not help, because the timer ignores how fast the day is running. Overshoot the look you wanted and each long beard can be crafted back down a stage. The beard also tints itself to your current hair color, so a trip to the salon changes it too.

The outfit points at Wilson from Don't Starve, which is why the beard is the centerpiece rather than the clothes, and the tooltip borrows the tone of that game's line about beard hair.