Does the "Game of Thrones" browned butter pie crust technique make any sense?
Any kind of crust that doesn't use cold fat could be made with brown butter easily. You can make crust by melting butter (with water and oil) then adding flour, and it's flaky - though not exactly the same texture as you get with cold fat. So just do that, except brown the butter first.

Or you could brown the butter, cool it til solid, and make a crust with a more normal recipe. I don't know if I've seen a pie crust calling for that, but I've seen it in cookies. I doubt it'd be exactly the same texture as with unmodified cold butter, because you lose some of the fat crystal structure in the butter, but it'd probably still be fine, and it'd taste like brown butter, which I assume is the goal.