The most "fair" chess setup

It's well known that according to engines, white has roughly half a pawn's advantage. I messed around in the analysis tool to try to get a board set up whereby adjusting material odds, the advantage is close to +0.00... replacing the king's bishop with a knight got it fairly close, but not exactly. Now, I was wondering, can anybody here create a board that does exactly this, or at least as close as possible? (and no, before you ask: a guaranteed draw doesn't count. It should also be fairly aesthetically pleasing, not just a mess of pieces.) I think this would be very interesting to see!

this board is given as +0.38 on chess.com but Stockfish gives it as 0.00.