Today's faction is based on the Way of the Sun Soul monk from Xanathar's Guide to Everything. As an anime fan, the Way of the Sun Soul sure looks to me like a saiyin from Dragon Ball Z, which immediately brings Vegeta to mind, so let's create a group of super-serious, heavily muscled monks.
Some monks stay in their monasteries and focus on their studies, secluded from the bustling markets of civilization.
Not the Order of the Searing Sun.
Heavily muscled, red-robed monks stride purposefully down the dusty streets of the city. They stop at an unoccupied corner. Two sit, setting out their conical hats in front of them, while the third proceeds to challenge all comers to a simple unarmed bout: the first fall loses. No challenger defeats him. Passers-by toss occasional coppers into the offered hats.
After one particularly rousing fight, the fighting monk abruptly sits, just like the others, while one of his companions rises and speaks to the crowd. He preaches of the importance of strength, of the innate desire of all living things to improve themselves and defend themselves or others. He talks of growing things yearning towards the sun and how heat forges metal into useful tools. He says that anyone wishing to join them may offer themselves to the Temple of the Flaring Candle twenty miles outside the city. Then all three monks stand, smoothly pocketing the change they collected, and move on.
A serious, unforgiving order of monks devoted to physical labor, the Order of the Searing Sun grew dramatically over the past few decades.
As a friendly faction, the monks are simply a serious order of hermits who need supplies as much as anyone else.
As a foe faction, a few years ago the monks began exerting control over the populations near their monasteries. They invite themselves to council meetings and spend inordinate amounts of time as guests of local nobles, offering firm advice and acting quite annoyed if it isn't taken. Communities without strong personalities leading them have found themselves essentially run by the monks, who in recent months have begun requesting "mandatory donations" from the population for the upkeep of their monastery.
- (Friend) As the PCs wander through the city, they're approached by a Monk of the Searing Sun. He's heard of a giant lizard that's known to wrestle its foes to the ground and nests a few days' travel away. The monks in his monastery wish to use the beast to test their wrestling prowess and he offers a reasonable sum to the party if they'll bring an adult; he throws enough coin on top of that to pay for chains and rental of a mule and wagon for a week.
- (Foe) The PCs enter a town where the locals act nervous. Half a dozen Searing Sun monks stride purposefully through its streets on various errands, and locals scurry out of their way. If the PCs don't ask about this, they're approached by a tanner who explains that the monks set up a monastery nearby a few years ago, then invited themselves to local council meetings, then began insisting on changes, then began essentially running the meetings, and now effectively run the town. They demand donations for extravagant expansions of their monastery. The tanner says that the townspeople will reward a group of adventurers who stand up to the monks and defeat them. The monks need not be killed; a thorough defeat will shame the monks into leaving.
- (Foe) The PCs enter a town that's bustling with nervous activity. A stage is under constructed in the market square. Turns out a group of monks from the Order of the Searing Sun arrived in town and announced a tournament...with control of the town as prize! If they defeat all comers, they will claim the town as their bounty and tax the locals heavily for construction of a monastery. Now the PCs just need to defeat the monks in one-on-one unarmed combat....