For someone who wants to get into jazz, I might start with these 5 drummer-led groups:

Tim Daisy's Vox Arcana
Harris Eisenstadt's Canada Day Quintet
Charles Rumback Trio
Tomas Fujiwara & The Hook Up
Devin Gray's Dirigo Rataplan

Or these trumpet-led groups:

Lina Allemano Titanium Riot
Jaimie Branch's Fly Or Die
Nate Wooley Quintet
Taylor Ho Bynum Sextet
Susana Santos Silva Impermanence

Maybe they're a saxophone/reeds person:

Tim Berne's Snakeoil
Jason Stein's Locksmith Isidore
Angelika Niescier Trio
Silke Eberhard Trio
Nick Mazzarella Trio

For delightfully unexpected and funky (a.k.a. weird) jazz:

DR. MiNT
São Paulo Underground
Natural Information Society
Peter Evans Quintet
Steve Lehman & Sélébéyone

Sometimes I think, people just want to know jazz is still alive and has deep, reflective thoughts about the world:

Mike Reed's Flesh & Bone
Fay Victor's SoundNoiseFUNK
Irresistible Entanglements
Matana Roberts COIN COIN series
Darius Jones MAN'ISH BOY epic

Truly, not enough folks push Mostly Other People Do the Killing when someone requests jazz recommendations.

Very few contemporary jazz composers are as wryly anarchic as Moppa Elliott. and most of them are in or have played in MOPDtK.