Search found 3 matches: Spike Jonze

Zach Braff
Jared Hess
Charlie Kaufmann
Michel Gondry
Rian Johnson
Pascal Laugier
Tate Taylor
Jason Reitman
Adam McKay
Joseph Kosinski
Gareth Evans
Prachya Pinkaew
Judd Apatow
Sung-Hee Jo
Deab Deblois
Joss Whedon
Mark Neveldine & Brian Taylor
Nima Nourizadeh
Jeong-beom Lee
Sam Fell


...too easy. All of those fulfil the requirements, but I don't know if I'd call any of them great. Maybe Zach Braff, but only as a writer/director. Or Jeong-beom Lee.

Or Spike Jonze, who didn't make the cut anyway, because he didn't wait a year to make Being John Malkovich. :>

There are many. For me, any director who produces one masterpiece (10/10) is great--and I have eleven of those from this century. But without a second tier 9 (9/10 for me, which is also tier 10), there are only Three:

Ridley Scott: Gladiator, The Counselor (10/10), and The Martian (9/10)
Christopher Nolan: Inception (10/10) and Interstellar, The Dark Knight, Memento (9/10).
Kantheryn Bigelow: Zero Dark Thirty (10/10), and The Hurt Locker (9/10).

But since I went ahead and dug the others up, I'll list them too:

Marc Webb--500 Days of Summer
Craig Brewer--Black Snake Moan
Gavin O'Connor--The Accountant (10+/10, my most perfect movie)
Spike Jonze--Her (10+/10, my most important movie)
Ang Lee--Life of Pi
Frank Whaley--Like Sunday, Like Rain
Coen Brothers--O Brother Where Art Thou!
Walter Hill--Undisputed

Filmmakers with multiple notable films that have started since 2000 that are very good:

Alfredson, Tomas (Let the Right One In, Tinker Tailor Soldier Spy)*
Bong Joon-Ho (Memories of Murder, The Host, Mother)
Castaing-Taylor, Lucien (Leviathan, Sweetgrass)
Dominik, Andrew (The Assassination of Jesse James by the Coward Robert Ford, Killing Them Softly)
Glazer, Johnathan (Under the Skin, Birth)*
Green, David Gordon (George Washington, All the Real Girls)*
Kaufman, Charlie (Synecdoche New York, Anomalisa)
Lanthimos, Giorgos (Dogtooth, Alps, The Lobster)*
Madsen, Michael (Into Eternity, The Visit)*
Oppenheimer, Joshua (The Act of Killing, The Look of Silence)*
Paravel, Verena (Leviathan, Foreign Parts)
Park Chan-wook (Oldboy, Stoker)*
Perry, Alex Ross (The Color Wheel, Listen Up Philip, Queen of Earth)
Strickland, Peter (Berberian Sound Studio, The Duke of Burgundy)
Weerasethakul, Apatchitpong (Tropical Malady, Syndromes and a Century, Uncle Boonmee)*
West, Ti (The House of the Devil, The Innkeepers)
Wright, Edgar (Shaun of the Dead, Hot Fuzz, Scott Pilgrim, The World's End)

* = meets your criteria for me

The 2000 cut-off seems arbitrary, as it ignores people who just started a few years earlier but have produced their best stuff in the 21st century: Paul Thomas Anderson, Spike Jonze, Noah Baumbach, Kim Ki-Duk, Kim Ji-Woon, Wes Anderson, Nicholas Winding Refn, Lynne Ramsay, the Dardennes, Kelly Reichardt, Jafar Panahi, off the top of my head.

If I had to put money down on which will have the most relevance in the future, I'd go Weerasethakul, Kaufman, Perry.