Back in 2010, noisms posted a piece on fighting large groups vs. single large enemies. In his experience, D&D is often paired with the first method, where encounters are against groups of monsters, with single foes only appearing as rare boss fights.
I'm more interested in the second approach, which he titles "Giant Slaying": rare encounters with large, threatening, and unique single enemies. In my opinion, this could be expanded even further into a monster of the week style game, where entire adventures are built around a single monster.
Each of these adventures are split into two portions: the chase and the kill. For some monsters, the chase is the hard part, while others are easy to find, but difficult to kill.
For example, I used the Forge to create 4 monster names: Soul Halcyon, Pale Antler Dragon, Needler Heart, and the Lotus Beak Wyrm.
All of these are meant to be difficult fights for 1st or 2nd level parties, so stat accordingly.
The Soul Halcyon is an infection as much as it is a monster. It spreads between people, connecting a hyper-empathic hivemind: the infected are so nice they'll point you towards the Soul Halcyon itself: the problem is catching up to it.
The Chase: The Soul Halcyon's physical form is fast, but the hive will point you straight to it. The Soul Halcyon will seek large population centers to infect.
The Kill: The Soul Halcyon's speed continues to reward it in combat: it's twice as fast as a man, and can fly short distances. Along with melee attacks, its scream forces WIS saves to resist inclusion into the hivemind (treat as a Dominate Person spell).
Pale Antler Dragon
The Pale Antler Dragon doesn't fit in the forests it lives in: it only feels comfortable when its wide spines scrape against the trees.
The Kill: Getting the Pale Antler Dragon into a straight fight mandates trickery and traps to stop it from barreling over a tree and vanishing into the forest. When finally cornered, the Pale Antler Dragon is a violent melee combatant, throwing PCs across the forest with wide sweeps of its horns and crushing them with its claws.
The Needler Heart is an immobile construct buried underground, slowly infecting the earth with spiked tunnels and fractal pathways.
The Chase: Navigating the maze-like passages around the Heart takes time as they shift around you: every round there's a 1-in-6 chance they flail wildly, requiring DEX checks to avoid the waving spikes.
The Kill: The Needler Heart is immobile but surrounded by writhing spikes: cutting them off is easy, but they attack you freely as long as you're in range. The Heart can grow spikes from the floor to effectively remove parts of the terrain, or attack directly by extending a massive needle.
The Lotus Beak Wyrm's scales flake off constantly, creating a hallucinogenic haze around it, that remains as it moves through the mountains its made home.
The Chase: Following the Lotus Beak Wyrm directly only gets the PCs more lost as the hallucinogens set in.
The Kill: The Wyrm is very lightly armored, but the combination of the waving fronds on its body and the hallucinations create a very unpleasant environment to fight. The hallucinogens are deactivated by water: shoving the Wyrm into a lake or stream will make it far easier to kill or capture.