The
Theme Workshop is required to craft a theme for your living quarters and/or diners based off of one of the four factions from Fallout 4: Brotherhood of Steel (BoS), the Institute, Minutemen, or Railroad faction.
Note: I found that my chances of finding fragments increased after building the Theme Workshop, although it is possible of finding pieces beforehand.
How to find fragments: 1) Sending Dwellers into the Wasteland
2) During Quest (
Requires Overseer's Office)
3) Spend Nuke-Cola Quantum to find all 9 pieces for a theme*
*I personally would recommend working towards other achievements, such as
Legend of the Wastes, before spending your quantum.
Wasteland What I've been doing is sending out 1 or 2 dwellers that have max stats out into the wasteland for a day or two (Don't forget to equip them with gear, including max stimpaks). When they return, or are overloaded with items and are forced to return, they normally have been gathering at least 3 pieces of a random recipe each run.
Overseer's Office (Quest)The overseer's office is required to do quest. Each quest will have varying levels of difficultly and/or prerequisites (including level or stat requirements for the dwellers eligible to take it on).
Just remember that when you arrive at at quest location don't forget to search every room for items before returning to your vault. This can also help you receive the achievement for
Big Pharma.
Good luck on your hunt!