50/34 compact with 11-32 10-speed Shimano 105 - will 11-34 make climbing easier or change chainring
You are already pretty close to the limit of what can be achieved easily.  You could certainly stick a 34t cassette on there, but it's not going to make any appreciable difference over a 32t.

The next step is a 36t cassette, which is likely to need a MTB rear mech (9 speed XT mech works well with 10s road shifters).

Another thing you can consider is a subcompact 46/30 chainset.  Making both changes would give you a 30/36 gear ratio, which is extremely low for a road bike.

If you know your target power (z1 for a recovery ride) you can use the following websites to calculate the gear ratio you need.

http://bikecalculator.com/
https://www.bikecalc.com/speed_at_cadence