Hi Michael,
You’ll need to re-check all this if travel is after 5th March.
Simplest fares are Hackney Central to Shenfield £9.10 and Shenfield to Brondesbury £4.45, total £13.55. You won’t get close to any of the caps by making two journeys both avoiding zone 1, apart from zones 1-9. That option involves splitting at Brentwood both ways and using a second discounted Oyster card. Zone 1-9 cap £9.30 plus £1.80 plus £1.15, total £12.25. It’s not the cheapest though.
The best I can find involves splitting at Manor Park which is helpfully zone 3/4. You would pay £2.00 plus £6.00 plus £2.40 plus £1.15, total £11.55. You can use one card because no caps are involved. The only other dual zoned station is Stratford but the total is £14.10. Any other split would inolve paying for a zone twice.
I imagine the places will be the same after March 5th, but the fares will be a little more.