I will take a crack at this, having had it every year, and being a bit of a fanboy of theirs. I won't be brewing it any time soon, but maybe somebody will find it useful.
This assumes a 25L batch to end up with enough for a 19L keg after losses to dry hops and trub.
Grist:
45% Golden Promise
33% Wheat Malt
11% Flaked Oats
11% Faked Wheat
Mash at 67C, single infusion.
Target 1.081 OG.
This grist should come out around 5SRM, which by my eye is pretty close to where Putty is.
Hopping:
Boil: None
Whirlpool: (for ten minutes at around 90C)
100g Azacca
100g Mosaic
This should net around 45IBUs, Putty is bitter, but not only from IBUs, it's also bitter from dry hopping, with that slighlty green edge.
Dry Hopping (these should all be pellet hops):
At high Krausen:
75g Mosaic
75g Azacca
100g Galaxy
Once FG Reached:
200g Galaxy
Fermentation:
Having had a good chat with Adam at Verdant whilst at Hop City 2018 I can tell you that as of then they were fermenting London Ale III at 19C, ramping to 23C over the last few days as the final dry hop is added.
Final gravity should be 1.019, which I had measured from a can of Putty over the weekend.