Not sure how many of these count as deep cuts, but here are a few from the last decade (or so) that I enjoyed:

Pontypool-Actually came out in 2008, but it's still worth watching, especially if you are looking for a zombie film that does something different. A washed-up radio DJ listens from his booth as his town breaks down around him following an outbreak of a mysterious infection. It definitely leans more toward psychological horror rather than traditional zombie horror, so I could see someone complaining that it's slow and doesn't really show anything until near the end.

Butterfly Kisses- A found footage film about a film student investigating a found footage film. Maybe a bit too meta for some, but I enjoy a found-footage movie that doesn't take itself too seriously. It seeds just enough doubt about whether the footage is "real" that it leaves you guessing how it's going to end.

Triangle-2009 film about a group of friends who come across a seemingly abandoned ocean liner while out on the water and decide to explore it. Maybe not that deep a cut, but it's worth checking out if you've never seen it.

Coherence- Not actually sure if this counts as horror. I see it classed as a sci-fi thriller a lot, but I found it while searching for something similar to Triangle. A group of friends gets together for a dinner party only to notice strange things happening after watching a comet passing overhead. It's hard to say anymore without spoiling it. Another one that could be seen as slow and without a lot of "real" scares. Still might be worth checking out if you want something that is slow-burn and more psychological.